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 = 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) 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
$x=2\lambda +5=0$
$\Rightarrow \lambda =-5/2,$
Since, $y=\lambda (1-b)+1=\frac{17}{2}$
$-\frac{5}{2}(1-b)+1=\frac{17}{2}$
b=4.
Also, $z=\lambda (a-1)+a=-\frac{13}{2}\Rightarrow a=6.$