Generating...                               quiz01_n11

  1. Let $\mathbf{a}$ = [ 1 , -2 , 5 ] and $\mathbf{b}$ = [ 4 , -1 , 2 ] . Find $4 \mathbf{a} + 3 \mathbf{b}$.

    [ 16 ,   − 11 ,  26 ] [ 20 ,   − 8 ,  26 ] [ 20 ,   − 11 ,  26 ] [ 16 ,   − 8 ,  26 ]

  2. Let $\mathbf{a} =$ [ 0 , -1 , -3 ] . Find $\vert\mathbf{a}\vert$.

    3 $\displaystyle \sqrt{11}$ $\displaystyle \sqrt{5}$ $\displaystyle \sqrt{10}$

  3. Let $\mathbf{a}$ = [ 0 , 1 , -1 ] and $\mathbf{b}$ = [ 1 , -1 , 2 ] . Find proj$_{\mathbf{a}}\mathbf{b}$.

    [ 1 ,  1 ,  0 ] [ 0 ,  0 ,  0 ] [ 0 ,   − 1 ,  1 ] $\displaystyle \left[ 0 , -\frac{3}{2} , \frac{3}{2} \right] $

  4. Suppose that $\vert\mathbf{a}\vert = 5$ and $\vert\mathbf{b}\vert = 3$, and that $\theta = \frac{3\,\pi}{4}$ is the angle between $\mathbf{a}$ and $\mathbf{b}$. Find $\vert\mathbf{a}\times\mathbf{b}\vert$.

    $\displaystyle \frac{21}{2}$ $\displaystyle \frac{21}{\sqrt{2}}$ $\displaystyle \frac{15}{\sqrt{2}}$ $\displaystyle \frac{15}{2}$

  5. $\mathbf{a}$ = [ 0 , 2 , 3 ] and $\mathbf{b}$ = [ -1 , 3 , -2 ] are

    $\displaystyle$    not orthogonal $\displaystyle$    orthogonal

  6. Let $\mathbf{a}$ = [ -4 , 1 , 1 ] and $\mathbf{b}$ = [ -5 , -3 , -4 ] . Find $\mathbf{a}\cdot\mathbf{b}$.

    8 14 13 9

  7. $\mathbf{a}$ = [ -2 , 3 , -3 ] , $\mathbf{b}$ = [ 3 , -1 , 0 ] , and $\mathbf{c}$ = [ 2 , 18 , -24 ] are

    $\displaystyle$    not coplanar $\displaystyle$    coplanar

  8. Let $\mathbf{a}$ = [ 0 , 3 , -1 ] and $\mathbf{b}$ = [ -4 , 3 , -5 ] . Find ${\mathbf{a}}\times\mathbf{b}$.

    [  − 12 ,  4 ,  12 ] [  − 11 ,  4 ,  12 ] [  − 12 ,  9 ,  15 ] [  − 11 ,  9 ,  16 ]

  9. Let $\mathbf{a}$ = [ 0 , -3 , 4 ] and $\mathbf{b}$ = [ -2 , 1 , 3 ] . Find comp$_{\mathbf{a}}\mathbf{b}$.

    $\displaystyle \frac{9}{5}$ $\displaystyle \frac{6}{5}$ $\displaystyle \frac{8}{\sqrt{35}}$ $\displaystyle \frac{10}{\sqrt{35}}$

  10. Let A [ -3 , 5 , 4 ] , B [ -6 , 8 , 1 ] , and C [ -7 , 6 , 4 ] . Find the area of triangle ABC.

    $\displaystyle \frac{3\,\sqrt{26}}{2}$ $\displaystyle \frac{\sqrt{253}}{2}$ $\displaystyle \sqrt{61}$ $\displaystyle \frac{6^{\frac{3}{2}}}{2}$


Department of Mathematics
Last modified: 2025-12-21