Question

The line passing through the points $(5,1,a)$ and $(3,b,1)$ crosses yz plane at the point $\left(0,\frac{17}{2},\frac{-13}{2}\right)$, then

• A. $a=2,b=8$
• B. $a=4,b=6$
• C. $a=6,b=4$
• D. $a=8,b=2$

Answer 1

Answer: (C)

Equation of line will be
$\frac{x-5}{2}=\frac{y-1}{1-b}=\frac{z-a}{a-1}$
$\Theta$ Point of intersection with $yz$-plane $x=0$
$\frac{-5}{2}=\frac{y-1}{1-b}=\frac{z-a}{a-1}$
$\therefore \frac{-5}{2}(1-b)+1=\frac{17}{2}\Rightarrow 5b-3=17\Rightarrow b=4$
$\text{ and }\frac{-5}{2}(a-1)+a=\frac{-13}{2}\Rightarrow -3a+5=-13\Rightarrow a=6$