Question

Let $yz$-plane divides the line joining $A(2,4,5)$ and $B(3,5,-4)$ in the ratio $-2:3$. Then find the point of intersection .

Answer 1

Given $A(x_1,y_1,z_1)=(2,4,5)$

$B(x_2,y_2,z_2)=(3,5,-4)$

$yz-$plane divide the line joining $A$ and $B$ in ratio

$=-x_1:x_2\to -2:3$

$=l:m$

Point of Intersection

$=[\frac{{lx}_2+{mx}_1}{l+m},\frac{{ly}_2+{my}_1}{l+m},\frac{{lz}_2+{mz}_1}{l+m}]$

$=[\frac{-2\left(3\right)+3\left(2\right)}{-2+3},\frac{-2\left(5\right)+3\left(4\right)}{-2+3},\frac{-2(-4)+3\left(5\right)}{-2+3}]$

$=[\frac{-6+6}{1},\frac{-10+12}{1},\frac{8+15}{1}]$

$=(0,2,23)$