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 $A = [1;0;0]$, $B = [2;0;0]$, $D = [3;-2;0]$, $E = [2;1;5]$.

$10$

$12$

$15$

$20$