Question

The ratio in which the joint of $(2,1,5),(3,4,3)$ is divided by the plane $2x+2y-2z-1=0$

• A. $5:12$
• B. $12:5$
• C. $5:7$
• D. $7:5$

Answer 1

Answer: (C)

$5:7$

Let P point lie on a plane $2x+2y-2z-1=0$and divide $(2,1,5),(3,4,3)$ in a ratio of $\lambda :1$
by section formula
P=($\frac{3\lambda +2}{\lambda +1},\frac{4\lambda +1}{\lambda +1},\frac{3\lambda +5}{\lambda +1}$)
put co-ordinate of P in plane equation
2$(\frac{3\lambda +2}{\lambda +1}+\frac{4\lambda +1}{\lambda +1}-\frac{3\lambda +5}{\lambda +1})$=1
by solving above equation,
we get,
$\lambda =\frac{5}{7}$