Question

The x coordinate of a point on the line joining the points P(2,2,1) and Q(5,1,-2) is 4.Find its z-coordinate.

Answer 1

Equation of line PQ:$\frac{x-2}{3}=\frac{y-2}{-1}=\frac{z-1}{-3}=\lambda .$

Coordinates of any random point on the line PQ is $(3\lambda +2,-\lambda +2,-3\lambda +1)$.

As x coordinate of a point on the line PQ is 4 so,$(3\lambda +2=4\Rightarrow \lambda =\frac{2}{3})$.

So,z coordinate is $-3\lambda +1=-3\left(\frac{2}{3}\right)+1=-1$.