Question

Coordinates of a point $P$ lying on the line $\frac{x-2}{4}=\frac{y-1}{3}=\frac{z+1}{2}$ such that the line joining the points $P$ and $A(3,1,5)$ is parallel to the plane $4x-2y+z=0$, is

• A. $(2,1,-1)$
• B. $(\frac{16}{3},\frac{7}{2},\frac{2}{3})$
• C. $(4,\frac{5}{2},0)$
• D. $(3,\frac{7}{4},\frac{-1}{2})$

Answer 1

The correct option is B $(\frac{16}{3},\frac{7}{2},\frac{2}{3})$

\( 4 x-2 y+z \)
Let coordinates of $P$ be $(4\lambda +2,3\lambda +1,2\lambda -1)$
Direction ratios of $AP$ are $<4\lambda -1,3\lambda ,2\lambda -6>$
$\Rightarrow 4(4\lambda -1)-2\left(3\lambda \right)+1(2\lambda -6)=0$
$\lambda =\frac{5}{6}$
$\therefore P\equiv (\frac{16}{3},\frac{7}{2},\frac{2}{3})$