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Question

Mathematics Question on Three Dimensional Geometry

The equation of the plane passing through the point (1,1,1)(1, 1, 1) and perpendicular to the planes $2

A

$14

B

$14

C

$14

D

$-14

Answer

$14

Explanation

Solution

Let direction ratios of normal be n⃗\vec{n}
⇒n⃗=∣i^j^k^ 21−2 3−6−2∣=−14i^−2j^−15k^\Rightarrow \vec{n}=\begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\\ 2 & 1 & -2 \\\ 3 & -6 & -2\end{vmatrix}=-14 \hat{i}-2 \hat{j}-15 \hat{k}
⇒\Rightarrow equation of plane is
−14(x−1)−2(y−1)−15(z−1)=0-14(x-1)-2(y-1)-15(z-1)=0
⇒14x+2y+15z=31\Rightarrow 14 x+2 y+15 z=31