A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as…
Mathematics20244 marksShort answer
A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as a plane having points $A(1, 0, 2)$, $B(3, -1, 1)$ and $C(1, 2, 1)$ on it. The mobile tower is tied with three cables from the points $A$, $B$ and $C$ such that it stands vertically on the ground. The top of the tower is at point $P(2, 3, 1)$ as shown in the figure below. The foot of the perpendicular from the point $P$ on the plane is at the point $Q\left(\frac{43}{29}, \frac{77}{29}, \frac{9}{29}\right)$.
Answer the following questions:
(i)
Find the equation of the plane containing the points $A$, $B$ and $C$.
