Generating...                               quiz01_n18

  1. Let A [ -5 , 1 , 0 ] , B [ -4 , -1 , 5 ] , and C [ -1 , 0 , 2 ] . Find the area of triangle ABC.

    $\displaystyle \frac{\sqrt{374}}{2}$ $\displaystyle 2\,\sqrt{21}$ $\displaystyle \frac{\sqrt{293}}{2}$ $\displaystyle \sqrt{101}$

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

    $\displaystyle -\frac{4}{\sqrt{10}}$ $\displaystyle \frac{3}{\sqrt{14}}$ $\displaystyle -\frac{7}{\sqrt{10}}$ $\displaystyle -\frac{1}{\sqrt{14}}$

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

    $\displaystyle \sqrt{10}$ $\displaystyle \sqrt{13}$ $\displaystyle \sqrt{14}$ $\displaystyle 2^{\frac{3}{2}}$

  4. Suppose that $\vert\mathbf{a}\vert = 3$ and $\vert\mathbf{b}\vert = 2$, and that $\theta = \frac{\pi}{4}$ is the angle between $\mathbf{a}$ and $\mathbf{b}$. Find $\vert\mathbf{a}\times\mathbf{b}\vert$.

    $\displaystyle 3\,\sqrt{2}$ $\displaystyle 5\,\sqrt{2}$ $\displaystyle 3^{\frac{3}{2}}$ $\displaystyle 5\,\sqrt{3}$

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

    [  − 1 ,   − 11 ,  13 ] [  − 1 ,   − 6 ,  13 ] [  − 4 ,   − 11 ,  13 ] [  − 4 ,   − 6 ,  13 ]

  6. $\mathbf{a}$ = [ 1 , -3 , -2 ] , $\mathbf{b}$ = [ -1 , -2 , 3 ] , and $\mathbf{c}$ = [ 16 , 2 , -42 ] are

    $\displaystyle$    coplanar $\displaystyle$    not coplanar

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

    $\displaystyle \left[ \frac{1}{3} , \frac{1}{6} , \frac{1}{6} \right] $ $\displaystyle \left[ \frac{4}{3} , \frac{2}{3} , \frac{2}{3} \right] $ $\displaystyle \left[ \frac{9}{7} , \frac{3}{7} , \frac{6}{7} \right] $ $\displaystyle \left[ \frac{3}{7} , \frac{1}{7} , \frac{2}{7} \right] $

  8. Let $\displaystyle z^2-6\,z+y^2+8\,y+x^2+2\,x+17=0$ . Find center and radius for the equation of sphere.

    The center is [  − 1 ,   − 4 ,  3 ] and the radius is 3 The center is [  − 1 ,   − 4 ,  3 ] and the radius is 4 The center is [  − 1 ,   − 3 ,  3 ] and the radius is 3 The center is [  − 1 ,   − 3 ,  3 ] and the radius is 4 The center is [  − 1 ,   − 4 ,  4 ] and the radius is 3 The center is [  − 1 ,   − 4 ,  4 ] and the radius is 4

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

    6 7 4 9

  10. Suppose that $\vert\mathbf{a}\vert = 2$ and $\vert\mathbf{b}\vert = 3$, and that $\theta = \frac{3\,\pi}{4}$ is the angle between $\mathbf{a}$ and $\mathbf{b}$. Find $\mathbf{a}\cdot\mathbf{b}$.

    $\displaystyle -3\,2^{\frac{3}{2}}$ $\displaystyle -3\,\sqrt{2}$ $\displaystyle 3\,\sqrt{2}$ $\displaystyle 3\,2^{\frac{3}{2}}$


Department of Mathematics
Last modified: 2026-07-16