Question

If the line $\frac{x-1}{1}=\frac{y+1}{-2}=\frac{z+1}{\lambda }$ lies in the plane $3x-2y+5z=0$ then $\lambda$ is

• A. $1$
• B. $-\frac{7}{5}$
• C. $\frac{5}{7}$
• D. no possible value

Answer 1

Answer: (B)

$-\frac{7}{5}$

We have equation of plane,

$3x-2y+5z=\mathrm{0.......}\left(1\right)$

We have line,

$\frac{x-1}{1}=\frac{y+1}{-2}=\frac{z+1}{\lambda }=\mu ......\left(2\right)$

General point on line is,

$P=(\mu +1,-2\mu -1,\lambda \mu -1)$

Since line (2) lies on line plane (1),so point P satisfy equation (1)

Therefore,

$3(\mu +1)-2(2\mu -1)+5(\lambda \mu -1)=0$

$3\mu +3+4\mu +2+5\mu \lambda -5=0$

$7\mu +5\mu \lambda =0$

$\lambda =\frac{-7}{5}$

Therefore option (B) is Correct.