MathsGee Homework Help Q&A - Recent questions tagged euclidean
https://mathsgee.com/tag/euclidean
Powered by Question2AnswerVerify that the Cauchy-Schwarz inequality holds. (a) \(\mathbf{u}=(-3,1,0), \mathbf{v}=(2,-1,3)\) (b) \(\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)\)
https://mathsgee.com/35875/verify-cauchy-schwarz-inequality-mathbf-mathbf-mathbf-mathbf
Verify that the Cauchy-Schwarz inequality holds.<br />
<br />
(a) \(\mathbf{u}=(-3,1,0), \mathbf{v}=(2,-1,3)\)<br />
<br />
(b) \(\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)\)Mathematicshttps://mathsgee.com/35875/verify-cauchy-schwarz-inequality-mathbf-mathbf-mathbf-mathbfFri, 14 Jan 2022 09:59:16 +0000Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
https://mathsgee.com/35854/verify-that-cauchy-schwarz-inequality-holds-mathbf-mathbf
Verify that the Cauchy&ndash;Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$Mathematicshttps://mathsgee.com/35854/verify-that-cauchy-schwarz-inequality-holds-mathbf-mathbfThu, 13 Jan 2022 09:13:52 +0000Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$
https://mathsgee.com/35853/verify-that-cauchy-schwarz-inequality-holds-mathbf-mathbf
Verify that the Cauchy&ndash;Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$Mathematicshttps://mathsgee.com/35853/verify-that-cauchy-schwarz-inequality-holds-mathbf-mathbfThu, 13 Jan 2022 09:13:03 +0000Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$
https://mathsgee.com/35852/verify-that-cauchy-schwarz-inequality-holds-mathbf-mathbf
Verify that the Cauchy&ndash;Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$Mathematicshttps://mathsgee.com/35852/verify-that-cauchy-schwarz-inequality-holds-mathbf-mathbfThu, 13 Jan 2022 09:12:11 +0000Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y)$ that satisfy the stated condition.
https://mathsgee.com/35851/mathbf-vector-describe-vectors-mathbf-satisfy-stated-condition
Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y)$ that satisfy the stated condition. (a) $\left\|\mathbf{r}-\mathbf{r}_{0}\right\|=1$ (b) $\left\|\mathbf{r}-\mathbf{r}_{0}\right\| \leq 1$ (c) $\left\|\mathbf{r}-\mathbf{r}_{0}\right\|>1$Mathematicshttps://mathsgee.com/35851/mathbf-vector-describe-vectors-mathbf-satisfy-stated-conditionThu, 13 Jan 2022 09:11:15 +0000Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy
https://mathsgee.com/35848/nonzero-vectors-mathbf-orthogonal-direction-cosines-satisfy
Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy $$ \cos \alpha_{1} \cos \alpha_{2}+\cos \beta_{1} \cos \beta_{2}+\cos \gamma_{1} \cos \gamma_{2}=0 $$Mathematicshttps://mathsgee.com/35848/nonzero-vectors-mathbf-orthogonal-direction-cosines-satisfyThu, 13 Jan 2022 09:08:14 +0000Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 /(i+1)$. Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.
https://mathsgee.com/35845/mathbf-vector-component-vector-component-product-mathbf-mathbf
Let $\mathbf{u}$ be a vector in $R^{100}$ whose $i$ th component is $i$, and let $\mathbf{v}$ be the vector in $R^{100}$ whose $i$ th component is $1 /(i+1)$. Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.Mathematicshttps://mathsgee.com/35845/mathbf-vector-component-vector-component-product-mathbf-mathbfThu, 13 Jan 2022 09:04:24 +0000If $\mathbf{u}$ and $\mathbf{v}$ are orthogonal vectors in $R^{n}$ with the Euclidean inner product, then prove that $$ \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} $$
https://mathsgee.com/35820/mathbf-orthogonal-vectors-euclidean-product-mathbf-mathbf
If $\mathbf{u}$ and $\mathbf{v}$ are orthogonal vectors in $R^{n}$ with the Euclidean inner product, then prove that $$ \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} $$Mathematicshttps://mathsgee.com/35820/mathbf-orthogonal-vectors-euclidean-product-mathbf-mathbfThu, 13 Jan 2022 08:38:00 +0000Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonal
https://mathsgee.com/35818/show-that-mathbf-u-2-3-1-4-and-mathbf-v-1-2-0-1-are-orthogonal
Show that $\mathbf{u}=(-2,3,1,4)$ and $\mathbf{v}=(1,2,0,-1)$ are orthogonalMathematicshttps://mathsgee.com/35818/show-that-mathbf-u-2-3-1-4-and-mathbf-v-1-2-0-1-are-orthogonalThu, 13 Jan 2022 08:35:03 +0000What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
https://mathsgee.com/35816/what-the-distance-d-between-the-point-left-right-line-0in
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$Mathematicshttps://mathsgee.com/35816/what-the-distance-d-between-the-point-left-right-line-0inThu, 13 Jan 2022 08:32:51 +0000Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
https://mathsgee.com/35814/prove-that-the-distance-d-between-the-point-left-right-plane
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is $$ D=\frac{\left|a x_{0}+b y_{0}+c z_{0}+d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} $$Mathematicshttps://mathsgee.com/35814/prove-that-the-distance-d-between-the-point-left-right-planeThu, 13 Jan 2022 08:31:09 +0000Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
https://mathsgee.com/35812/find-the-distance-d-between-the-point-4-3-and-the-plane-2-1
Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.Mathematicshttps://mathsgee.com/35812/find-the-distance-d-between-the-point-4-3-and-the-plane-2-1Thu, 13 Jan 2022 08:29:41 +0000The planes $$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7 $$ are parallel since their normals, $(1,2,-2)$ and $(2,4,-4)$, are parallel vectors. Find the distance between these planes.
https://mathsgee.com/35810/parallel-normals-parallel-vectors-distance-between-planes
The planes $$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7 $$ are parallel since their normals, $(1,2,-2)$ and $(2,4,-4)$, are parallel vectors. Find the distance between these planes.Mathematicshttps://mathsgee.com/35810/parallel-normals-parallel-vectors-distance-between-planesThu, 13 Jan 2022 08:27:48 +0000Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.
https://mathsgee.com/35809/show-that-mathbf-v-a-b-and-mathbf-w-b-a-are-orthogonal-vectors
Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.Mathematicshttps://mathsgee.com/35809/show-that-mathbf-v-a-b-and-mathbf-w-b-a-are-orthogonal-vectorsThu, 13 Jan 2022 08:26:58 +0000Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
https://mathsgee.com/35807/do-the-points-and-form-the-vertices-of-right-triangle-explain
Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.Mathematicshttps://mathsgee.com/35807/do-the-points-and-form-the-vertices-of-right-triangle-explainThu, 13 Jan 2022 08:25:35 +0000A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?
https://mathsgee.com/35804/sailboat-travels-mathrm-exerts-force-mathrm-toward-northeast
A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?Mathematicshttps://mathsgee.com/35804/sailboat-travels-mathrm-exerts-force-mathrm-toward-northeastThu, 13 Jan 2022 08:23:17 +0000Let $\mathbf{u}$ and $\mathbf{v}$ be nonzero vectors in 2 - or 3 -space, and let $k=\|\mathbf{u}\|$ and $l=\|\mathbf{v}\|$. Prove that the vector $\mathbf{w}=l \mathbf{u}+k \mathbf{v}$ bisects the angle between $\mathbf{u}$ and $\mathbf{v}$.
https://mathsgee.com/35803/nonzero-vectors-mathbf-mathbf-mathbf-bisects-between-mathbf
Let $\mathbf{u}$ and $\mathbf{v}$ be nonzero vectors in 2 - or 3 -space, and let $k=\|\mathbf{u}\|$ and $l=\|\mathbf{v}\|$.<br />
<br />
Prove that the vector $\mathbf{w}=l \mathbf{u}+k \mathbf{v}$ bisects the angle between $\mathbf{u}$ and $\mathbf{v}$.Mathematicshttps://mathsgee.com/35803/nonzero-vectors-mathbf-mathbf-mathbf-bisects-between-mathbfThu, 13 Jan 2022 08:22:31 +0000Find the lengths of the sides and the interior angles of the triangle in $R^{4}$ whose vertices are $$ P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5,7,2) $$
https://mathsgee.com/35800/lengths-sides-interior-angles-triangle-whose-vertices-quad
Find the lengths of the sides and the interior angles of the triangle in $R^{4}$ whose vertices are $$ P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5,7,2) $$Mathematicshttps://mathsgee.com/35800/lengths-sides-interior-angles-triangle-whose-vertices-quadThu, 13 Jan 2022 08:19:18 +0000The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is
https://mathsgee.com/35781/the-angle-between-vectors-1-3-2-and-4-2-1-is
The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is<br />
<br />
<br />
<br />
A) 0<br />
<br />
B) $\dfrac{\pi}{3}$<br />
<br />
C) $\dfrac{\pi}{2}$<br />
<br />
D) $\pi$<br />
<br />
E) none of the aboveMathematicshttps://mathsgee.com/35781/the-angle-between-vectors-1-3-2-and-4-2-1-isThu, 13 Jan 2022 07:56:40 +0000The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to
https://mathsgee.com/35780/the-distance-from-the-point-1-to-the-plane-2-x-10-11-is-equal-to
The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to<br />
<br />
<br />
<br />
A) $\dfrac{1}{3}$<br />
<br />
B) 3<br />
<br />
C) $\dfrac{1}{15}$<br />
<br />
D) 5<br />
<br />
E) none of the aboveMathematicshttps://mathsgee.com/35780/the-distance-from-the-point-1-to-the-plane-2-x-10-11-is-equal-toThu, 13 Jan 2022 07:55:41 +0000Determine whether planes $2 x+y+z-1=0,-x+3 y-2 z-3=0$ and $3 x-y=-1$ intersect. If yes, find the intersection.
https://mathsgee.com/35775/determine-whether-planes-intersect-find-the-intersection
Determine whether planes $2 x+y+z-1=0,-x+3 y-2 z-3=0$ and $3 x-y=-1$ intersect. If yes, find the intersection.Mathematicshttps://mathsgee.com/35775/determine-whether-planes-intersect-find-the-intersectionThu, 13 Jan 2022 07:51:06 +0000What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?
https://mathsgee.com/35759/what-the-distance-d-between-the-point-p-left-right-and-line
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?Mathematicshttps://mathsgee.com/35759/what-the-distance-d-between-the-point-p-left-right-and-lineThu, 13 Jan 2022 07:19:41 +0000The angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ is
https://mathsgee.com/35751/the-angle-between-vectors-2-6-4-and-4-2-1-is
The angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ is<br />
<br />
<br />
<br />
A. 0<br />
<br />
B. $\dfrac{\pi}{3}$<br />
<br />
C. $\dfrac{\pi}{2}$<br />
<br />
D. $\pi$<br />
<br />
E. none of the aboveMathematicshttps://mathsgee.com/35751/the-angle-between-vectors-2-6-4-and-4-2-1-isThu, 13 Jan 2022 07:04:27 +0000The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is
https://mathsgee.com/35735/the-angle-between-vectors-1-3-2-and-4-2-1-is
The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is<br />
<br />
<br />
<br />
A) 0<br />
<br />
B) $\frac{\pi}{3}$<br />
<br />
C) $\frac{\pi}{2}$<br />
<br />
D) $\pi$<br />
<br />
E) none of the aboveMathematicshttps://mathsgee.com/35735/the-angle-between-vectors-1-3-2-and-4-2-1-isThu, 13 Jan 2022 06:38:21 +0000The distance from the point $(-1,1,1)$ to the plane
https://mathsgee.com/35734/the-distance-from-the-point-1-1-1-to-the-plane
The distance from the point $(-1,1,1)$ to the plane $$ 2 x-10 y+11 z-4=0 $$ is equal to<br />
<br />
<br />
<br />
A) 3<br />
<br />
B) $\frac{1}{3}$<br />
<br />
C) 5<br />
<br />
D) $\frac{1}{5}$<br />
<br />
E) none of the aboveMathematicshttps://mathsgee.com/35734/the-distance-from-the-point-1-1-1-to-the-planeThu, 13 Jan 2022 06:37:20 +0000When are bases in Euclidean vector spaces V (Rⁿ or Cⁿ) topologically stable?
https://mathsgee.com/31908/when-are-bases-euclidean-vector-spaces-topologically-stable
When are bases in Euclidean vector spaces V (Rⁿ or Cⁿ) topologically stable?Mathematicshttps://mathsgee.com/31908/when-are-bases-euclidean-vector-spaces-topologically-stableThu, 26 Aug 2021 01:25:03 +0000What are normed spaces?
https://mathsgee.com/27514/what-are-normed-spaces
What are normed spaces?Mathematicshttps://mathsgee.com/27514/what-are-normed-spacesSat, 08 May 2021 05:05:30 +0000How do I describe a Euclidean space?
https://mathsgee.com/27508/how-do-i-describe-a-euclidean-space
How do I describe a Euclidean space?Mathematicshttps://mathsgee.com/27508/how-do-i-describe-a-euclidean-spaceSat, 08 May 2021 04:58:51 +0000Calculate the Euclidean distance between the points P(-2;-1) and Q(2;-6)
https://mathsgee.com/24708/calculate-the-euclidean-distance-between-the-points-p-2-and
Calculate the Euclidean distance between the points P(-2;-1) and Q(2;-6)Mathematicshttps://mathsgee.com/24708/calculate-the-euclidean-distance-between-the-points-p-2-andSun, 07 Feb 2021 02:56:50 +0000What is a key step in K-nearest neighbors?
https://mathsgee.com/21319/what-is-a-key-step-in-k-nearest-neighbors
What is a key step in K-nearest neighbors?Data Science & Statisticshttps://mathsgee.com/21319/what-is-a-key-step-in-k-nearest-neighborsTue, 27 Oct 2020 00:21:45 +0000How do I choose k when using k-nearest neighbor algorithm?
https://mathsgee.com/20946/how-do-i-choose-k-when-using-k-nearest-neighbor-algorithm
How do I choose k when using k-nearest neighbor algorithm?Data Science & Statisticshttps://mathsgee.com/20946/how-do-i-choose-k-when-using-k-nearest-neighbor-algorithmFri, 02 Oct 2020 08:43:28 +0000In k-NN what will happen when you increase/decrease the value of k?
https://mathsgee.com/16866/in-nn-what-will-happen-when-you-increase-decrease-the-value-of
In k-NN what will happen when you increase/decrease the value of k?Data Science & Statisticshttps://mathsgee.com/16866/in-nn-what-will-happen-when-you-increase-decrease-the-value-ofMon, 27 Jul 2020 18:43:41 +0000How does one choose between Euclidean and Manhattan distances when using k-NN algorithm?
https://mathsgee.com/16863/choose-between-euclidean-manhattan-distances-using-algorithm
How does one choose between Euclidean and Manhattan distances when using k-NN algorithm?Data Science & Statisticshttps://mathsgee.com/16863/choose-between-euclidean-manhattan-distances-using-algorithmMon, 27 Jul 2020 12:44:13 +0000Given a dataset, show me how Euclidean Distance works in three dimensions.
https://mathsgee.com/438/given-dataset-show-euclidean-distance-works-three-dimensions
Given a dataset, show me how Euclidean Distance works in three dimensions.Data Science & Statisticshttps://mathsgee.com/438/given-dataset-show-euclidean-distance-works-three-dimensionsMon, 11 Mar 2019 10:20:03 +0000