Question

The equation of plane passing through a point $A (2,-1,3)$ and parallel to the vectors $a =(3,0,-1)$ and $b =(-3,2,2)$ is:

• A. 2x - 3y + 6z - 25 = 0
• B. 2x - 3y + 6z + 25 = 0
• C. 3x - 2y + 6z - 25 = 0
• D. 3x - 2y + 6z + 25 = 0

Answer 1

Answer: (A)

2x - 3y + 6z - 25 = 0

Answer 2

Let the DR of the normal of required plane be $< a, b, c >$ Since plane is parallel to $(3,0,-1)$ $\therefore$ normal must be perpendicular $\therefore 3 a +0 b - c =0 \ldots$ (1) Also, it is parallel to $(-3,2,2)$ $\therefore-3 a +2 b +2 c =0 \ldots$ (2) From (1) and (2) $\frac{a}{2}=\frac{-b}{6-3}=\frac{c}{6}$ $a=2, b=-3, c=6$ It passes through $(2,-1,3)$ $2(x-2)-3(y+1)+6(z-3)=0$ $\Rightarrow 2 x-4-3 y-3+6 z-18=0$ $\Rightarrow 2 x-3 y+6 z-25=0$