Question

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

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

Answer 1

Answer: (B)

$a=6,b=4$

Equation of the line through the points $(5,1,a)$ & $(3,b,1)$ is
$\frac{x-5}{3-5}=\frac{y-1}{b-1}=\frac{z-a}{1-a}=\lambda$
Now it passes through $(0,\frac{17}{2},\frac{-13}{2})$
$\therefore \frac{0-5}{-2}=\frac{17/2-1}{b-1}=\frac{-13/2-a}{1-a}=\lambda$

$\Rightarrow \lambda =\frac{5}{2}$
$\therefore \frac{17/2-1}{b-1}=\frac{5}{2}$

$\Rightarrow b=4$
and $\frac{-13/2-a}{1-a}=\frac{5}{2}$

$\Rightarrow a=6$