Generating...                               quiz01_n12

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

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

  2. Let $\displaystyle z^2+4\,z+y^2+6\,y+x^2+2\,x+13=0$ . Find center and radius for the equation of sphere.

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

  3. Let $\mathbf{a} =$ [ 3 , -5 , 0 ] . Find $\vert\mathbf{a}\vert$.

    $\displaystyle \sqrt{35}$ $\displaystyle \sqrt{34}$ $\displaystyle \sqrt{41}$ 5

  4. Let $\mathbf{a}$ = [ -3 , -2 , -3 ] and $\mathbf{b}$ = [ 2 , 1 , 0 ] . Find $4 \mathbf{a} + 5 \mathbf{b}$.

    [  − 2 ,  2 ,   − 12 ] [ 2 ,   − 3 ,   − 12 ] [  − 2 ,   − 3 ,   − 12 ] [ 2 ,  2 ,   − 12 ]

  5. $\mathbf{a}$ = [ 1 , -2 , -4 ] and $\mathbf{b}$ = [ -18 , -9 , 0 ] are

    $\displaystyle$    orthogonal $\displaystyle$    not orthogonal

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

    $\displaystyle \frac{35\,\sqrt{3}}{2}$ $\displaystyle \frac{35}{2}$ $\displaystyle \frac{25\,\sqrt{3}}{2}$ $\displaystyle \frac{25}{2}$

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

    [ 12 ,   − 20 ,  12 ] [ 12 ,   − 16 ,  12 ] [ 14 ,   − 16 ,  10 ] [ 14 ,   − 20 ,  9 ]

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

    $\displaystyle -\frac{10}{3^{\frac{3}{2}}}$ $\displaystyle -\frac{9}{\sqrt{37}}$ $\displaystyle -\frac{8}{3^{\frac{3}{2}}}$ $\displaystyle -\frac{10}{\sqrt{37}}$

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

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

  10. $\mathbf{a}$ = [ 1 , -3 , 2 ] , $\mathbf{b}$ = [ -1 , 0 , -2 ] , and $\mathbf{c}$ = [ -3 , 15 , -21 ] are

    $\displaystyle$    not coplanar $\displaystyle$    coplanar


Department of Mathematics
Last modified: 2026-02-06