Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Equation of the line through the given points is $\frac{x-3}{5-3}=\frac{y-4}{1-4}=\frac{z-1}{6-1}$ $\Rightarrow \frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-1}{5}$ Any point on this line can be taken as $(3+$ $2\lambda ,4-3\lambda ,1+5\lambda )$ If this point lies on XY-plane then the z-coordinate is zero $$\Rightarrow 1+5\lambda =0\Rightarrow \lambda =-\frac{1}{5}$$ Thus the required coordinates of the point are $$\left(3-\frac{2}{5},4-3\left(-\frac{1}{5}\right),0\right)\equiv \left(\frac{13}{5},\frac{23}{5},0\right)$$