Question

Equation of the line of the shortest distance between the lines $\frac{x}{1} = \frac{y}{-1} = \frac{z}{1}$ and $\frac{x-1}{0} = \frac{y+1}{-2} = \frac{z}{1}$ is :

• A. $\frac{x}{1} = \frac{y}{-1} = \frac{z}{-2}$
• B. $\frac{x-1}{1} = \frac{y+1}{-1} = \frac{z}{-2}$
• C. $\frac{x-1}{1} = \frac{y+1}{-1} = \frac{z}{-1}$
• D. $\frac{x}{-2} = \frac{y}{1} = \frac{z}{2}$

Answer 1

The Correct Option is B

$\begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\1 & -1 & 1 \\0 & -2 & 1\end{vmatrix}$
$\frac{x}{1}=\frac{y}{-1}=\frac{z}{1}$

$\frac{x-1}{0}=\frac{y+1}{-2}=\frac{z}{1} $
$\frac{1-\lambda}{1}=\frac{-1-2 \mu+\lambda}{-1}=\frac{\mu-\lambda}{-2} $
$-2=3 \lambda+\mu $
$-1+\lambda=-1-2 \mu+\lambda $
$\mu=0 $
$ \lambda=-\frac{2}{3}$