Question

A straight line joining the points $(1,1,1)$ and $(0,0,0)$ intersects the plane $2x+2y+z=10$ at

• A. $(1,2,5)$
• B. $(2,2,2)$
• C. $(2,1,5)$
• D. $(1,1,6)$

Answer 1

The correct option is B $(2,2,2)$

Equation of line passing through $(0,0,0)$ and $(1,1,1)$ is given by,

$\frac{x-0}{1-0}=\frac{y-0}{1-0}=\frac{z-0}{1-0}$

$\Rightarrow \frac{x}{1}=\frac{y}{1}=\frac{z}{1}=t$ (say)

So any point on the above line is taken as $(t,t,t)$

To get the point of intersection of line and the plane $2x+2y+z=10$

Above point will satisfy the plane as well

$\Rightarrow 2t+2t+t=10\Rightarrow 5t=10\Rightarrow t=2$

Hence the point of intersection is $(t,t,t)=(2,2,2)$