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 $P_x+P_y+P_z=$

• A. $6$
• B. $-8$
• C. $8$
• D. $0$

Answer 1

Answer: (C)

$8$

Equation of line $AB$ is given by,

$\frac{x-1}{-2-1}=\frac{y-2}{3-2}=\frac{z-3}{4-3}=t$ (say)

$\Rightarrow \frac{x-1}{-3}=\frac{y-2}{1}=\frac{z-3}{1}=t$

So any point on the line AB is given by, $P=(1-3t,t+2,t+3)$

So for intersection of $AB$ with $zx$ plane put $y$-coodinate zero.

$\Rightarrow t+2=0\Rightarrow t=-2$

$\therefore P=(7,0,1)$

Hence, $P_x+P_y+P_z=7+0+1=8$