Question
A plane intersects the coordinate axes at the points (1, 0, 0), (0, 2, 0), and (0, 0, -3). The obtained plane equation is ax + by + 3z − d = 0. What is the value of d? (A) −3 (B) −6 (C) −9 (D) 3
Answers
mathhelper
sub each given point into ax + by + 3z − d = 0
(1,0,0) ---> x + 0 + 0 - d = 0 , x = d
(0,2,0) ---> 0 + 2b + 0 - d = 0, d = 2b
(0,0,-3) ---> 0 + 0 + 3(-3) - d = 0 , d = -9
(1,0,0) ---> x + 0 + 0 - d = 0 , x = d
(0,2,0) ---> 0 + 2b + 0 - d = 0, d = 2b
(0,0,-3) ---> 0 + 0 + 3(-3) - d = 0 , d = -9