# Recent questions tagged vectors

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Determine whether the statements are true or false, and justify your answer
Find the lengths of the sides and the interior angles of the triangle in $R^{4}$ whose vertices are $$P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5,7,2)$$
Find the lengths of the sides and the interior angles of the triangle in $R^{4}$ whose vertices are $$P(2,4,2,4,2), \quad Q(6,4,4,4,6), \quad R(5,7,5,7,2)$$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 ... close 0 answers 4 views Express the vector \mathbf{u}=(2,3,1,2) in the form \mathbf{u}=\mathbf{w}_{1}+\mathbf{w}_{2}, where \mathbf{w}_{1} is a scalar multiple of \mathbf{a}=(-1,0,2,1) and \mathbf{w}_{2} is orthogonal to a. Express the vector \mathbf{u}=(2,3,1,2) in the form \mathbf{u}=\mathbf{w}_{1}+\mathbf{w}_{2}, where \mathbf{w}_{1} is a scalar multiple of \m ... 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 form of vector and parametric equations of lines in R^{2} and R^{3} 1 answer 4 views What is the form of vector and parametric equations of lines in R^{2} and R^{3}What is the form of vector and parametric equations of lines in R^{2} and R^{3} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a formula in terms of n for \sum_{r=1}^{n}\left(3 r^{2}+r-2\right). Simplify your answer fully. 0 answers 6 views Find a formula in terms of n for \sum_{r=1}^{n}\left(3 r^{2}+r-2\right). Simplify your answer fully. Find a formula in terms of n for \sum_{r=1}^{n}\left(3 r^{2}+r-2\right). Simplify your answer fully. &nbsp; NB: You may find the following ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the sum of the first three terms of  \sum_{r=1}^{n}\left(3 r^{2}+r-2\right) 0 answers 2 views Find the sum of the first three terms of  \sum_{r=1}^{n}\left(3 r^{2}+r-2\right)\begin{aligned} &amp;\text { Find the sum of the first three terms of } \sum_{r=1}^{n}\left(3 r^{2}+r-2\right) \text {. } \end{aligned} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \underline{a}=(2,1,-1) and \underline{b}=(-1,2,1), then 2 \underline{a}-3 \underline{b} is equal to 0 answers 5 views 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 &nbsp; A) (1,-4,-5) B) (7,-4,5) C ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The angle between vectors (1,3,-2) and (4,-2,-1) is 0 answers 7 views The angle between vectors (1,3,-2) and (4,-2,-1) isThe angle between vectors (1,3,-2) and (4,-2,-1) is &nbsp; A) 0 B) \dfrac{\pi}{3} C) \dfrac{\pi}{2} D) \pi E) none of the above ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to 0 answers 4 views 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 &nbsp; A) \dfrac{1}{3} B) 3 C) \dfrac{1}{15} D) 5 E) no ... close 0 answers 6 views Let z_{1}=\left|z_{1}\right|\left(\cos \left(\theta_{1}\right)+i \sin \left(\theta_{1}\right)\right) and z_{2}=\left|z_{2}\right|\left(\cos \left(\theta_{2}\right)+i \sin \left(\theta_{2}\right)\right) be two complex numbers.Let z_{1}=\left|z_{1}\right|\left(\cos \left(\theta_{1}\right)+i \sin \left(\theta_{1}\right)\right) and z_{2}=\left|z_{2}\right|\left(\cos \left(\ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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. 0 answers 4 views 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.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. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Match the reasons to the lines of the following proof. 0 answers 8 views Match the reasons to the lines of the following proof. Match the reasons to the lines of the following proof. Let T be a triangle with vertices u, v, and w in \mathrm{C} where the vertices are n ... close 0 answers 9 views 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 product of A, B and C? 0 answers 3 views What is the product of A, B and C? \text { Given } A=\left\begin{array}{ll} 4 &amp; 5 \end{array}\right, B=\left\begin{array}{llll} 1 &amp; 1 &amp; 2 &amp; 1 \end{ar ... 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}\right) and the line a x+b y+c=0 in R^2? 1 answer 4 views 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?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? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 You may choose the same option for matching more than once. Read through the following proof and match the lines with the reasons given below. 0 answers 5 views You may choose the same option for matching more than once. Read through the following proof and match the lines with the reasons given below. You may choose the same option for matching more than once.&nbsp;Read through the following proof and match the lines with the reasons given below. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines L 1 to L 5. 0 answers 3 views You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines L 1 to L 5. You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines L 1 to L 5. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The angle between vectors (2,6,-4) and (4,-2,-1) is 0 answers 6 views The angle between vectors (2,6,-4) and (4,-2,-1) isThe angle between vectors (2,6,-4) and (4,-2,-1) is &nbsp; A. 0 B. \dfrac{\pi}{3} C. \dfrac{\pi}{2} D. \pi E. none of the above ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let a, b and c be vectors in \mathrm{R}^{3}, \times denotes the cross product, . the dot product. Which of the following is false? 0 answers 7 views Let a, b and c be vectors in \mathrm{R}^{3}, \times denotes the cross product, . the dot product. Which of the following is false?Let a, b and c be vectors in \mathrm{R}^{3}, \times denotes the cross product, . the dot product. Which of the following is false? A. -a \time ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let a, b and c be vectors in \mathrm{R}^{3}, such that a \cdot(b \times c)=0. Then 0 answers 8 views Let a, b and c be vectors in \mathrm{R}^{3}, such that a \cdot(b \times c)=0. ThenLet a, b and c be vectors in \mathrm{R}^{3}, such that a \cdot(b \times c)=0. Then A. a, b and c are colinear B. a, b and c lie on t ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \vec{a} and \vec{b} be non-zero, non parallel vectors. Identify proj \vec{a} \vec{b} geometrically in the diagram. 0 answers 4 views Let \vec{a} and \vec{b} be non-zero, non parallel vectors. Identify proj \vec{a} \vec{b} geometrically in the diagram. Let \vec{a} and \vec{b} be non-zero, non parallel vectors. Identify proj \vec{a} \vec{b} geometrically in the diagram. &nbsp; &nbsp; ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The complex number \frac{1-2 i}{1+2 i} is equal to 0 answers 5 views 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 &nbsp; A) \dfrac{3}{5}+\dfrac{4}{5} i B) -\dfrac{3}{5}+\dfrac{4}{5} i C) \dfrac{3}{5}-\ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 &nbsp; A) (1,-4,-5) B) (7,-4,5) C) (7,-4,-5) D) (7,4, ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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 &nbsp; A) 0 B) \frac{\pi}{3} C) \frac{\pi}{2} D) \pi E) none of the above ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (-1,1,1) to the plane 0 answers 5 views 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 &nbsp; A) 3 B) $\frac{1}{3}$ C) 5 D) $\frac{1}{5}$ E) no ...