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Recent questions tagged vectors


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Determine whether the statements are true or false, and justify your answer
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What is the form of vector and parametric equations of lines in $R^{2}$ and $R^{3}$
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Find a formula in terms of $n$ for $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$. Simplify your answer fully.
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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.   NB: You may find the following ...
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Find the sum of the first three terms of $ \sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$
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Find the sum of the first three terms of $ \sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$\begin{aligned} &\text { Find the sum of the first three terms of } \sum_{r=1}^{n}\left(3 r^{2}+r-2\right) \text {. } \end{aligned} ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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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
(102,810 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
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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
(102,810 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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Match the reasons to the lines of the following proof.
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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 ...
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asked in Mathematics Jan 13
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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 ...
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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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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.
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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 $L 5$.

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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
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asked in Mathematics Jan 13
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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?
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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}$, such that $a \cdot(b \times c)=0$. Then
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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 ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jan 13
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Let $\vec{a}$ and $\vec{b}$ be non-zero, non parallel vectors. Identify proj $\vec{a} \vec{b}$ geometrically in the diagram.
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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
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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
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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 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
(102,810 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) $\frac{\pi}{3}$ C) $\frac{\pi}{2}$ D) $\pi$ E) none of the above ...
by MathsGee Platinum
(102,810 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
(102,810 points)
asked in Mathematics Jan 13
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