Generating...                               quiz01_n12

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

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

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

    $\displaystyle -\sqrt{6}$ $\displaystyle -\frac{7}{\sqrt{10}}$ $\displaystyle -\sqrt{6}$ $\displaystyle -\frac{8}{\sqrt{10}}$

  3. $\mathbf{a}$ = [ 3 , -3 , 3 ] , $\mathbf{b}$ = [ 0 , -2 , 2 ] , and $\mathbf{c}$ = [ 6 , 6 , -18 ] are

    $\displaystyle$    coplanar $\displaystyle$    not coplanar

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

    $\displaystyle \left[ -\frac{48}{25} , \frac{36}{25} , 0 \right] $ $\displaystyle \left[ -\frac{39}{19} , \frac{39}{19} , \frac{13}{19} \right] $ $\displaystyle \left[ -\frac{52}{25} , \frac{39}{25} , 0 \right] $ $\displaystyle \left[ -\frac{39}{19} , \frac{39}{19} , \frac{13}{19} \right] $

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

    $\displaystyle -\frac{15}{\sqrt{2}}$ $\displaystyle -\frac{25}{\sqrt{2}}$ $\displaystyle \frac{25}{\sqrt{2}}$ $\displaystyle \frac{15}{\sqrt{2}}$

  6. $\mathbf{a}$ = [ -4 , 2 , 3 ] and $\mathbf{b}$ = [ 10 , 2 , 12 ] are

    $\displaystyle$    orthogonal $\displaystyle$    not orthogonal

  7. Let A [ -4 , 3 , -5 ] , B [ -5 , 2 , 0 ] , and C [ -4 , 6 , -6 ] . Find the area of triangle ABC.

    $\displaystyle \frac{19}{2}$ $\displaystyle \frac{\sqrt{206}}{2}$ $\displaystyle \frac{3\,\sqrt{42}}{2}$ 7

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

    9 4 7 6

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

    $\displaystyle 3^{\frac{3}{2}}$ $\displaystyle \sqrt{22}$ $\displaystyle \sqrt{22}$ $\displaystyle \sqrt{34}$

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

    [ 4 ,  12 ,   − 15 ] [ 4 ,  12 ,   − 12 ] [ 4 ,  16 ,   − 17 ] [ 4 ,  16 ,   − 21 ]


Department of Mathematics
Last modified: 2025-10-30