Question

Let the co - ordinates of the point where the line joining the points $(2,-3,1),(3,-4,-5)$ cuts the plane $2x+y+z=7$ be $(x,y,z)$. Find $x+y+z$ ?

Answer 1

D.R.'s of the line are $x_2-x_1,y_2-y_1,z_2-z_1$ or $1,-1,-6$
It passes through $(2,-3,1).$
Hence, the equations are $\frac{x-2}{1}=\frac{y+3}{-1}=\frac{z-1}{-6}=r,$ say.
The co-ordinates of any point on this line are $r+2,-r-3,1-6r$
Also this points lie on the plane $2x+y+z=7$
$\Rightarrow 2r+4-r-3-6r+1=7$

$\therefore r=-1.$
Substituting the value of $r$, we get the co - ordinates of the required point as $(1,-2,7).$

Hence, $x+y+z=6$.