Question

If the lines
$\stackrel{→}{r}= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )$
and
$\stackrel{→}{r} = ( \alpha \hat{i} - \hat{j} ) + μ( \hat{2j} - \hat{3k} )$
are co-planer , then the distance of the plane containing these two lines from the point $( α , 0 , 0 )$ is :

• A. $\frac{2}{9}$
• B. $\frac{2}{11}$
• C. $\frac{4}{11}$
• D. 2

Answer 1

Answer: (B)

$\frac{2}{11}$

Answer 2

The correct answer is (B) : $$$\frac{2}{11}$

∵ Both lines are coplanar, so
$\begin{vmatrix} \alpha-1 & 0 & -1 \\\ 0 & 3 & -1 \\\ 2 & 0 & -3\\\ \end{vmatrix}$= 0
$⇒ α = \frac{5}{3}$
Equation of plane containing both lines
$\begin{vmatrix} x-y & y+1 & z-1 \\\ 0 & 3 & -1 \\\ 2 & 0 & -3\\\ \end{vmatrix}$= 0
$⇒ 9x + 2y + 6z = 13$
So , distance of ( 5/3 , 0 ,0) from this plane
$= \frac{2}{\sqrt{81+4+26}} = \frac{2}{11}$