Analytic Geometry Answers

Q.No.1 Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,-4) and R(6,-2,-5) is right-angled.

1. A farmer wants to dig a circular reservoir for water storage. He decided to have it 10- feet wide in diameter. Is there a need for a mango tree that is located at coordinates (-4, 2) from the center of the reservoir to be removed? Support your answer.

2. Satellite dishes are usually shaped like a paraboloid, where each cross section is a parabola. This shape of the dish allows radio signals coming in parallel to the axis of the dish to bounce off the surface and meet at the focus. Hence, the receiver should be placed at the focus for a good signal reception. How far should the receiver be from the vertex if the satellite dish is 14 ft across and 5.2 ft deep at the vertex?