Question

The equation of the plane passing through the points (3,2,2) and (1,0,-1) and parallel to the line $\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}$, is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is D

None of these

Equation of plane passing through the point (1,0,-1) is,
$a(x-1)+b(y-0)+c(z+1)=0\cdots \left(i\right)$
Also, plane (i) is passing through (3,2,2)
$\therefore a(3-1)+b(2-0)+c(2+1)=0$
$or2a+2b+3c=0\cdots \left(i\right)$
$line\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}$
$\therefore 2a-2b+3c=0\cdots \left(ii\right)$
From (i) and (ii), $\frac{a}{-3}=\frac{b}{0}=\frac{c}{2}$
Therefore, the required plane is,
$-3(x-1)+0(y-0)+2(z+1)=0$
$or-3x+2z+5=0$