C

1103040206

Level: 
C
Given the points $A = [1,5]$ and $B = [-4,2]$, specify all the points $C$ lying on the $x$-axis, such that the area of the triangle $ABC$ is $14$. Hint: Use a cross product of vectors.
$C_1=[2,0],\ C_2=\left[-\frac{50}3,0\right]$
$C_1=[1,0],\ C_2=\left[-\frac{47}3,0\right]$
$C_1=[2,0],\ C_2=\left[-\frac{47}3,0\right]$
$C_1=[1,0],\ C_2=\left[-\frac{50}3,0\right]$

1003040201

Level: 
C
We are given the vectors $\vec{a}=(-1, 2,3)$, $\vec{b}=(3, 1, -2)$ and $\vec{c}=(1, 2,-1)$. Find the coordinates of a vector $\vec{v}$, such that $\vec{v}$ is perpendicular to both vectors $\vec{a}$ and $\vec{b}$, while $\vec{v}\cdot\vec{c}=12$ holds.
$\vec{v}=(-6,6,-6)$
$\vec{v}=(6,-6,6)$
$\vec{v}=(-7,7,-7)$
$\vec{v}=(7,-7,7)$