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 $(2,2,2)$

The Cartesian equation of line through the points $(1,1,1)$ and
$(0,0,0)$ is,
$\frac{x-0}{1}=\frac{y-0}{1}=\frac{z-0}{1}=\lambda$
Let a point on the line $(k,k,k)$.
For the point of intesection, putting $(k,k,k)$ in the equation of plane,
$2k+2k+k=10$
$\Rightarrow k=2$
Therefore, the point of intersection is $(2,2,2)$