Question

Find the coordinates of the point where the line joining the points $(2,-3,1)$ and $(3,-4,-5)$ cuts the plane $2x+y+z=7$.

• A. (1, 2, - 7)
• B. (1, - 2, 7)
• C. (-1, - 2, 7)
• D. (1, 2, 7)

Answer 1

Answer: (B)

The direction ratios of the line are $3-2,-4-(-3),-5-1$
i.e. $1,-1,-6$
Hence equation of the line joining the given points.
is $\frac{x-2}{1}=\frac{y+3}{-1}=\frac{z-1}{-6}=r$ (say)
Coordinates of any point on this line are
$(r+2,-r-3,-6r+1)$
If this point lies on the given plane $2x+y+z=7$,
then $2(r+2)+(-r-3)+(-6r+1)=7$
$\Rightarrow r=-1$
Coordinates of any point on this line are
$(-1+2,-(-1)-3,-6(-1)+1)$ i.e. $(1,-2,7)$