Question

The equation of the plane passing through the points $(2,2,1)\&(9,3,6)$ and perpendicular to the plane $2x+6y+6z=1$ is.

• A. $2x-4y+5z-9=0$
• B. $3x+4y-x-5=0$
• C. $3x+4y-5z-9=0$
• D. $x+4y-9z-3=0$

Answer 1

Answer: (C)

$3x+4y-5z-9=0$

We have two points $P(2,2,1)Q(9,3,6)$
$n_1$ (Normal vector of given plane) $=(2\hat{i}+6\hat{j}+6\hat{k})$ and $\overrightarrow{PQ}=7\hat{i}+\hat{j}+5\hat{k}$
$n_2$ (Normal vector of required plane) $=\overrightarrow{n_1}\times \overrightarrow{PQ}$
$=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 6& 6\\ 7& 1& 5\end{array}\right|$
$=24\hat{i}+32\hat{j}-40\hat{k}$
Required equation of planes
$24(x-2)+32(y-2)-40(z-1)=0$
$3(x-2)+4(y-2)-5(z-1)=0$
$3x+4y-5z-9=0$ Equation of required plane