Question

Find the co-ordinates of the point of intersection of the line $\frac{x+1}{1}=\frac{y+3}{3}=\frac{z-2}{-2}$ with the plane $3x+4y+5z=5$.

Answer 1

$L:\frac{x+1}{1}=\frac{y+3}{3}=\frac{z-2}{2}$

Plane:$3x+4y+5z=5$

Let $P(x,y,z)=(r-1,3r-3,-2r+2)=5$ be the point on $L$ which intersect the plane.

$\therefore P(x,y,z)$ must satisfy equation of plane.

$3(r-1)+4(3r-3)+5(-2r+2)=5$

$\Rightarrow r=2$

$\therefore P(x,y,z)=(1,3,-2)$