Question

If line $\frac{x-2}{3}$ $=\frac{y-4}{4}$ $=\frac{z+2}{1}$is parallel to planes $\mu$ $x+3y-2z+d=0$ and $x-2$ $\lambda$ $y+z=0$, then value of $\lambda$ and $\mu$ are

• A. $\mu$ $=4$, $\lambda$ $=-\frac{2}{3}$
• B. $\mu$ $=-6$, $\lambda$ $=-2$
• C. $\mu$ $=\frac{-10}{3}$, $\lambda$ $=\frac{-1}{2}$
• D. $\mu$ $=\frac{-10}{3}$, $\lambda$ $=\frac{1}{2}$

Answer 1

Answer: (D)

$\mu$ $=\frac{-10}{3}$, $\lambda$ $=\frac{1}{2}$

Since line is parallel to the plane
$3\times \mu +4\times 3+1\times (-2)=0$
$\Rightarrow 3\mu =2-12$
$\mu =\frac{-10}{3}$ and $3\times 1+4\times (-2\lambda )+1\times 1=0$
$\Rightarrow -8\lambda =-4$

$\Rightarrow \lambda =\frac{1}{2}$