# Recent questions tagged vectors

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Use Head to Tail Method to represent the following vectors and finally draw Resultant vector.
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.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 $\mathbf{r}=(x, y) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfy 0 answers 7 views Show that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfyShow that two nonzero vectors$\mathbf{v}_{1}$and$\mathbf{v}_{2}$in$R^{3}$are orthogonal if and only if their direction cosines satisfy $$\cos \ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \|\mathbf{v}\|=2 and \|\mathbf{w}\|=3, what are the largest and smallest values possible for \|\mathbf{v}-\mathbf{w}\| ? Give a geometric explanation of your results. 0 answers 12 views If \|\mathbf{v}\|=2 and \|\mathbf{w}\|=3, what are the largest and smallest values possible for \|\mathbf{v}-\mathbf{w}\| ? Give a geometric explanation of your results.If \|\mathbf{v}\|=2 and \|\mathbf{w}\|=3, what are the largest and smallest values possible for \|\mathbf{v}-\mathbf{w}\| ? Give a geometric exp ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Are these statements True or False? 0 answers 10 views Are these statements True or False?(a) If each component of a vector in R^{3} is doubled, the norm of that vector is doubled. &nbsp; (b) In R^{2}, the vectors of norm 5 whose init ... close 0 answers 101 views 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}.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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 When are two nonzero vectors orthogonal to each other? 1 answer 20 views When are two nonzero vectors orthogonal to each other?When are two nonzero vectors orthogonal to each other? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that \mathbf{u}=(-2,3,1,4) and \mathbf{v}=(1,2,0,-1) are orthogonal vectors in R^{4}. 1 answer 11 views Show that \mathbf{u}=(-2,3,1,4) and \mathbf{v}=(1,2,0,-1) are orthogonal vectors in R^{4}.Show that \mathbf{u}=(-2,3,1,4) and \mathbf{v}=(1,2,0,-1) are orthogonal vectors in R^{4}. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let S=\{\mathbf{i}, \mathbf{j}, \mathbf{k}\} be the set of standard unit vectors in R^{3} . Show that each ordered pair of vectors in S is orthogonal. 1 answer 6 views Let S=\{\mathbf{i}, \mathbf{j}, \mathbf{k}\} be the set of standard unit vectors in R^{3} . Show that each ordered pair of vectors in S is orthogonal.Let S=\{\mathbf{i}, \mathbf{j}, \mathbf{k}\} be the set of standard unit vectors in R^{3} . Show that each ordered pair of vectors in S is ortho ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How do I determine the equation of a normal in R^2 or R^3? 1 answer 9 views How do I determine the equation of a normal in R^2 or R^3?How do I determine the equation of a normal in R^2 or R^3? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What are Orthogonal Projections? 1 answer 7 views What are Orthogonal Projections?What are Orthogonal Projections? ... close 1 answer 5 views close 1 answer 5 views Find the orthogonal projections of the vectors \mathbf{e}_{1}=(1,0) and \mathbf{e}_{2}=(0,1) on the line L that makes an angle \theta with the positive x-axis in R^{2}.Find the orthogonal projections of the vectors \mathbf{e}_{1}=(1,0) and \mathbf{e}_{2}=(0,1) on the line L that makes an angle \theta with the ... close 1 answer 5 views 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} $$If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}= ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\mathbf{u}=(-2,3,1,4)$and$\mathbf{v}=(1,2,0,-1)$are orthogonal 1 answer 2 views Show that$\mathbf{u}=(-2,3,1,4)$and$\mathbf{v}=(1,2,0,-1)$are orthogonalShow that$\mathbf{u}=(-2,3,1,4)$and$\mathbf{v}=(1,2,0,-1)$are orthogonal ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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} ?$1 answer 5 views What is the distance$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} ?$What is the distance$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} ?$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that, In$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$is 1 answer 8 views Prove that, In$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$isProve that, In$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 $$D=\frac{\left| ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. 1 answer 6 views Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1.Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. ... close 1 answer 3 views The planes$$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7 $$are parallel since their normals, (1,2,-2) and (2,4,-4), are parallel vectors. Find the distance between these planes.The planes$$ 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 d ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\mathbf{v}=(a, b)$and$\mathbf{w}=(-b, a)$are orthogonal vectors. 0 answers 4 views 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. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Do the points$A(1,1,1), B(-2,0,3)$, and$C(-3,-1,1)$form the vertices of a right triangle? Explain. 0 answers 3 views Do the points$A(1,1,1), B(-2,0,3)$, and$C(-3,-1,1)$form the vertices of a 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. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Is it possible to have$\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$Explain. 0 answers 2 views Is it possible to have$\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$Explain.Is it possible to have$\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$Explain. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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? 0 answers 2 views 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?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 ...