IB Mathematics Analysis and Approaches AHL 3.17—vector Equations of a Plane Questionbank

Find the vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$.

Find $\overrightarrow{AB} \times \overrightarrow{AC}$ using the cross product formula.

Find the area of triangle $ABC$.

Find the Cartesian equation of the plane containing $A$, $B$ and $C$.

Find the distance from the origin to this plane.

Verify that the point $P(1, 2, 1)$ lies on $\Pi_1$.

Find a vector equation of the line $L$ of intersection of $\Pi_1$ and $\Pi_2$.

Find the acute angle between $\Pi_1$ and $\Pi_2$.

Find the shortest distance from the origin $O$ to the plane $\Pi_1$.

Find the coordinates of the foot $M$ of the perpendicular from $O$ to $\Pi_1$.

Find the point of intersection of the line $L_1$ and the plane $\pi$.

Determine if the line $L_1$ is parallel, perpendicular, or neither to the normal of the plane $\pi$.