Generating...                               quiz01_n25

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

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

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

    3 $\displaystyle \sqrt{11}$ $\displaystyle \sqrt{14}$ $\displaystyle \sqrt{13}$

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

    [  − 21 ,   − 4 ,  6 ] [  − 16 ,   − 2 ,  2 ] [  − 16 ,   − 4 ,  4 ] [  − 21 ,   − 2 ,  3 ]

  4. Find the unit vector in the direction of [ -3 , 2 , 1 ] .

    $\displaystyle \left[ -\frac{3}{\sqrt{19}} , \frac{3}{\sqrt{19}} , \frac{1}{\sqrt{ 19}} \right] $ $\displaystyle \left[ -\frac{3}{\sqrt{14}} , \frac{2}{\sqrt{14}} , \frac{1}{\sqrt{ 14}} \right] $ $\displaystyle \left[ -\frac{2}{3} , \frac{2}{3} , \frac{1}{3} \right] $ $\displaystyle \left[ -\frac{3}{\sqrt{19}} , \frac{2}{\sqrt{19}} , \frac{2}{\sqrt{ 19}} \right] $

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

    10 $\displaystyle 14\,\sqrt{3}$ $\displaystyle 10\,\sqrt{3}$ 14

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

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

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

    $\displaystyle$    orthogonal $\displaystyle$    not orthogonal

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

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

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

    $\displaystyle \left[ -\frac{12}{17} , \frac{8}{17} , \frac{8}{17} \right] $ $\displaystyle \left[ -\frac{20}{21} , \frac{10}{21} , \frac{5}{21} \right] $ $\displaystyle \left[ -\frac{4}{3} , \frac{2}{3} , \frac{1}{3} \right] $ $\displaystyle \left[ -\frac{15}{17} , \frac{10}{17} , \frac{10}{17} \right] $

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

    6 9 4 7


Department of Mathematics
Last modified: 2025-06-19