Question

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

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

Answer 1

The correct option is C

$a=6,b=4$

Equation of line passing through
$(5,1,a)\text{and}(3,b,1)$ is
$\frac{x-5}{2}=\frac{y-1}{1-b}=\frac{z-a}{a-1}=\lambda .$
If line crosses yz-plane i.e., $x=0$
$\Rightarrow x=2\lambda +5=0$
$\Rightarrow \lambda =-5/2,$
Since, $y=\lambda (1-b)+1=\frac{17}{2}$
$-\frac{5}{2}(1-b)+1=\frac{17}{2}\Rightarrow b=4$
Also, $z=\lambda (a-1)+a=-\frac{13}{2}\Rightarrow a=6.$