Mathematics I20775 marksNumerical: Vector perpendicular to planeDot product and cross Product
Find a vector perpendicular to the plane that passes through the points: P(1, 4, 6), Q(-2, 5, -1) and R(1, -1, 1).
Find a vector perpendicular to the plane that passes through the points: $P(1, 4, 6)$, $Q(-2, 5, -1)$ and $R(1, -1, 1)$. [5]
- $P(1, 4, 6)$ - $Q(-2, 5, -1)$ - $R(1, -1, 1)$ A normal vector to the plane is the cross product of two vectors lying in the plane: $$\vec{n} = \overrightarrow{PQ} \times \overrightarrow{PR}$$ $$\overrightarrow{PQ} = Q - P = (-2-1,\ 5-4,\ -1-6) = (-3,\ 1,\ -7)$$ $$\overrightarrow{PR} = R - P = (...