Question

If $A=(-2,3,4),B=(1,2,3)$ are two points and P is the point of intersection of $AB$ and $zx-$ plane then $P_x+P_y+P_z=$

Answer 1

$AP:PB=-y_1:y_2=-3:2$
Negative ratio shows that point $P$ divides the line $AB$ externally in ratio $3:2$
$\Rightarrow P_x=\frac{3\cdot 1+2\cdot 2}{3-2}=7\Rightarrow P_y=\frac{3\cdot 2-2\cdot 3}{3-2}=0\Rightarrow P_y=\frac{3\cdot 3-2\cdot 4}{3-2}=1$
$\therefore P_x+P_y+P_z=7+0+1=8$