Question

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 (43/29, 77/29, 9/29) Answer the following questions.

A school is preparing the stage for its annual day function. They want to place a hanging mic and a hanging light on the stage. • They decide to position the mic at the point (3,2,1) such that it is equidistant from a plain backdrop and the hanging light as shown below. • The equation of the surface of the plain backdrop is 2x - y + z + 1 = 0

The distance of the point 2i + j − k from the plane r·(i − 2j + 4k) = 9 will be:

Find the image of the point (3,−2, 1) in the plane 3x − y + 4z = 2