Generating...                               quiz01_n22_n1

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

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

  2. $\mathbf{a}$ = [ 1 , 3 , 0 ] , $\mathbf{b}$ = [ 1 , -3 , 3 ] , and $\mathbf{c}$ = [ 27 , 15 , 12 ] are

    $\displaystyle$    coplanar $\displaystyle$    not coplanar

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

    [ 1 ,   − 2 ,  6 ] [ 1 ,   − 3 ,  10 ] [ 1 ,   − 2 ,  4 ] [ 1 ,   − 3 ,  7 ]

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

    [  − 14 ,   − 2 ,  7 ] [  − 16 ,   − 2 ,  7 ] [  − 16 ,   − 5 ,  7 ] [  − 14 ,   − 5 ,  7 ]

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

    $\displaystyle \left[ \frac{11}{9} , \frac{22}{9} , \frac{22}{9} \right] $ $\displaystyle \left[ \frac{8}{9} , \frac{16}{9} , \frac{16}{9} \right] $ [ 0 ,  2 ,  1 ] $\displaystyle \left[ 0 , \frac{14}{5} , \frac{7}{5} \right] $

  6. Let $\mathbf{a}$ = [ -1 , 4 , -1 ] and $\mathbf{b}$ = [ -1 , 5 , 0 ] . Find comp$_{\mathbf{a}}\mathbf{b}$.

    6 $\displaystyle 2^{\frac{5}{2}}$ $\displaystyle \frac{7}{\sqrt{2}}$ 5

  7. $\mathbf{a}$ = [ 3 , -1 , -4 ] and $\mathbf{b}$ = [ -19 , -12 , -12 ] are

    $\displaystyle$    orthogonal $\displaystyle$    not orthogonal

  8. Suppose that $\vert\mathbf{a}\vert = 1$ and $\vert\mathbf{b}\vert = 2$, and that $\theta = \frac{\pi}{6}$ is the angle between $\mathbf{a}$ and $\mathbf{b}$. Find $\mathbf{a}\cdot\mathbf{b}$.

    $\displaystyle \sqrt{3}$ 1 3 $\displaystyle 3^{\frac{3}{2}}$

  9. Suppose that $\vert\mathbf{a}\vert = 2$ and $\vert\mathbf{b}\vert = 3$, and that $\theta = \frac{\pi}{6}$ is the angle between $\mathbf{a}$ and $\mathbf{b}$. Find $\vert\mathbf{a}\times\mathbf{b}\vert$.

    12 6 3 6

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

    The center is [ 1 ,  0 ,   − 3 ] and the radius is 4 The center is [ 1 ,  1 ,   − 3 ] and the radius is 4 The center is [ 1 ,  0 ,   − 2 ] and the radius is 4 The center is [ 1 ,  0 ,   − 2 ] and the radius is 5 The center is [ 1 ,  0 ,   − 3 ] and the radius is 5 The center is [ 1 ,  1 ,   − 3 ] and the radius is 5


Department of Mathematics
Last modified: 2026-05-20