Question

Direction cosines of the normal to the plane containing the lines $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $\frac{x - 1}{2}=\frac{y - 1}{3}=\frac{z - 1}{5}$ are

• A. $\frac{2}{\sqrt{14}},\frac{- 3}{\sqrt{14}},\frac{5}{\sqrt{14}}$
• B. $\frac{2}{\sqrt{14}},\frac{- 3}{\sqrt{14}},\frac{1}{\sqrt{14}}$
• C. $\frac{2}{\sqrt{14}},\frac{- 1}{\sqrt{14}},\frac{1}{\sqrt{14}}$
• D. $\frac{3}{\sqrt{13}},\frac{- 2}{\sqrt{13}},1$

Answer 1

Answer: (B)

The normal vector to the plane $=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 3 & 5 \end{vmatrix}$
$=2\hat{i}-3\hat{j}+\hat{k}$
Hence, direction cosines are $\left(\frac{2}{\sqrt{14}} , \frac{- 3}{\sqrt{14}} , \frac{1}{\sqrt{14}}\right)$