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Recent questions tagged distance


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Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant?
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Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant?Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant? ...
by MathsGee Platinum
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asked in Mathematics Jan 15
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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 $R^{3} ?$
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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
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Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
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Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
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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?

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If $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal to
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If $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal toIf $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal to   A) $(1,-4,-5)$ B) $(7,-4,5)$ C ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is
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The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ isThe angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is   A) 0 B) $\dfrac{\pi}{3}$ C) $\dfrac{\pi}{2}$ D) $\pi$ E) none of the above ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to
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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal toThe distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to   A) $\dfrac{1}{3}$ B) 3 C) $\dfrac{1}{15}$ D) 5 E) no ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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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.
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What is the product of $A$, $B$ and $C$?
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What is the product of $A$, $B$ and $C$?\begin{equation} \text { Given } A=\left\begin{array}{ll} 4 & 5 \end{array}\right, B=\left\begin{array}{llll} 1 & 1 & 2 & 1 \end{ar ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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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 $R^2$?
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The angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ is
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The angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ isThe angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ is   A. 0 B. $\dfrac{\pi}{3}$ C. $\dfrac{\pi}{2}$ D. $\pi$ E. none of the above ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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The complex number $\frac{1-2 i}{1+2 i}$ is equal to
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The complex number $\frac{1-2 i}{1+2 i}$ is equal toThe complex number $\dfrac{1-2 i}{1+2 i}$ is equal to   A) $\dfrac{3}{5}+\dfrac{4}{5} i$ B) $-\dfrac{3}{5}+\dfrac{4}{5} i$ C) $\dfrac{3}{5}-\ ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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If $\vec{a}=(2,1,-1)$ and $\vec{b}=(-1,2,1)$, then $2 \vec{a}-3 \vec{b}$ is equal to
0 answers 9 views
If $\vec{a}=(2,1,-1)$ and $\vec{b}=(-1,2,1)$, then $2 \vec{a}-3 \vec{b}$ is equal toIf $\vec{a}=(2,1,-1)$ and $\vec{b}=(-1,2,1)$, then $2 \vec{a}-3 \vec{b}$ is equal to   A) $(1,-4,-5)$ B) $(7,-4,5)$ C) $(7,-4,-5)$ D) $(7,4, ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is
0 answers 4 views
The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ isThe angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is   A) 0 B) $\frac{\pi}{3}$ C) $\frac{\pi}{2}$ D) $\pi$ E) none of the above ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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The distance from the point $(-1,1,1)$ to the plane
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The distance from the point $(-1,1,1)$ to the planeThe distance from the point $(-1,1,1)$ to the plane $$ 2 x-10 y+11 z-4=0 $$ is equal to   A) 3 B) $\frac{1}{3}$ C) 5 D) $\frac{1}{5}$ E) no ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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Let $x^{2}+2 x \arctan y=y \cos x$. Find $y^{\prime}$ at $\left(\dfrac{\pi}{2},-1\right)$.
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Evaluate $\int \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$
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Determine whether the integral $\int_{0}^{1} \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ is convergent or divergent.
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Evaluate $\int_{1}^{2} \frac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$
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Evaluate $\int_{1}^{2} \frac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$Evaluate $\int_{1}^{2} \dfrac{x^{2}-x+4}{(x+1)\left(x^{2}+1\right)} d x=$   A. $\quad \ln \left(\frac{27}{20}\right)+\arctan 2-\frac{\pi}{4}$ ...
by MathsGee Platinum
(103,042 points)
asked in Mathematics Jan 13
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