Points and Vectors

2010015702

Level:

We are given the vectors $\vec{a}=(1,2,-3)$, $\vec{b}=(0,-1,2)$, and $\vec{c}=(-1,1,0)$. Find the mixed product $(\vec{a}\times\vec{b})\cdot\vec{c}$.

$ -3 $

The mixed product is not defined.

$ (0,-2,0) $

$ -2 $

Level:

Find the area of the parallelogram $ABCD$ where $A = [1,3,2]$, $B = [3,4,6]$, $D = [2,5,8]$.

$\sqrt{77}$

$8$

$2\sqrt{13}$

$\sqrt{94}$

Level:

Find the volume of the parallelepiped $ABCDEFGH$ where $A = [1,0,0]$, $B = [2,0,0]$, $D = [3,-2,0]$, $E = [2,1,5]$.

$10$

$12$

$15$

$20$