The equation of a plane is `2x-y-3z=5` and `A(1, 1, 1), B(2, 1, -3), C(1, -2, -2) and D(-3, 1, 2)` are four points, which of the following line segment are interesect by the plane?

Options

A. AD
B. AB
C. AC
D. BC

Answer

B, C, D

Explanation

For A(1,2,3), 2x-y-5=2-1-5`lt`0
For B(2,1,-3) 2x-y-3z-5=4-1+9-5 `lt` 0
For C(1,-2,-2), 2x-y-3z-5 = 2+2+6-5 `gt` 0
For D(-3,1,2), 2x-y-3z-5 = -6 -1 -6 -5 `lt` 0
`therefore` A,D are on the side of the plane and B,C are on the other side.
`therefore` The line segment AB, AC, BD and CD intersect the plane.