Question

CS 334 Final Exam Prof. Danyang Zhang Given the following plane equation, 4. and three points A(1, o, o), B(0.5, 0.3, 0.1), С(0.2, 0.5, 0.8), decide their locations relative to the given plane, i.e., in front of the plane? on the plane? or behind the plane? (10 points)

Answer 1

The relative location from the plane can be found out by substituting the coordinates of the points in the equation of the plane.

If the value comes out to be positive, it is on the same side of the plane, that is, in front of it.

If the value comes out to be negative, it is on the other side of the plane, that is, behind it.

If the value comes put to be 0, the point lies on the plane.

Given equation : x + y + z = 1

It can be written as : x + y + z - 1 = 0

Substituting (x,y,z) with :

a. A(1,0,0)

Gives, 1 + 0 + 0 - 1 = 0

Hence it lies on the plane.

b. B(0.5,0.3,0.1)

Gives, 0.5 + 0.3 + 0.1 - 1 = -0.2

As the values is negative, B lies behind the plane.

c. C(0.2,0.5,0.8)

Gives, 0.2 + 0.5 + 0.8 - 1 = 0.5

As the value is positive, C lies in front of the plane.