If the origin and the points P(2,3,4), Q(1,2,3) and R(x,y,z) are coplanar, then

Options

A. `x - 2y -z = 0`
B. `x+2y + z = 0`
C. `x- 2y + z = 0`
D. `2x- 2y + z = 0`

Answer

C

Explanation

Let `O(0,0,0)` be the origin.
It is given that `O(0,0,0), P(2,3,4), Q(1,2,3)` and `R(x,y,z)` are coplanar.
`:. [OR" "OP" "OQ]`
`|{:(x-0,y-0,z-0),(2-0,3-0,4-0),(1-0,2-0,3-0):}|=0`
`|{:(x,y,z),(2,3,4),(1,2,3):}| = 0`
`x(9-8) -y(6-4) +z(4-3) = 0`
`rArr x-2y + z = 0`