Question:
On which of the following lines lies the point
of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$
and the plane, $x+y+z=2$ ?
Correct Option: , 3
Solution:
General point on the given line is
$x=2 \lambda+4$
$y=2 \lambda+5$
$z=\lambda+3$
Solving with plane,
$2 \lambda+4+2 \lambda+5+\lambda+3=2$
$5 \lambda+12=2$
$5 \lambda=-10$
$\lambda=-2$
$\therefore$ Option $(3)$
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