Question

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

• A. $a=11,b=4$
• B. $a=8,b=2$
• C. $a=2,b=8$
• D. $a=4,b=6$

Answer 1

The correct option is A $a=11,b=4$

Equation of line passing through $(5,1,a)$ and $(3,b,1)$ is

$\frac{x-5}{2}=\frac{y-1}{1-b}=\frac{z-a}{a-b}=\lambda$

If line crosses $yz$-plane $i.e.,x=0$

$x=2\lambda +5=0$

$\Rightarrow \lambda =-\frac{5}{2},$

Since, $y=\lambda (1-b)+1\Rightarrow \frac{17}{2}=\frac{-5}{2}(1-b)+1\Rightarrow b=4$

Also, $z=\lambda (a-1)+a\Rightarrow -\frac{13}{2}=\frac{-5}{2}(a-1)+a\Rightarrow a=11$