the equationof 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 segments are intersects by the plane? (A) AD (B) AB (C) AC (D) BC

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.