A line drawn from a point $\mathrm{A}(-2,-2,3)$ and parallel to the line…
A line drawn from a point $\mathrm{A}(-2,-2,3)$ and parallel to the line $\frac{\mathrm{x}}{-2}=\frac{\mathrm{y}}{2}=\frac{\mathrm{z}}{-1}$ meets the $\mathrm{YOZ}-$ plane in point $\mathrm{P}$, then the co-ordinates of the point $\mathrm{P}$ are
$(0,4,-4)$
$(0,2,2)$
$(0,-2,2)$
$(0,-4,4)$
Solution
Equation of required lines is
$\frac{\mathrm{x}+2}{-2}=\frac{\mathrm{y}+2}{2}=\frac{\mathrm{z}-3}{-1}$ and this line meets $\mathrm{YZ}$ plane in $\mathrm{P}$.
Coordinates of any point on this line are $(-2 \lambda-21,2 \lambda-2,-\lambda+3)$, where $\lambda$ is a scalar.
Since $\mathrm{P}$ is on $\mathrm{YZ}$ plane, we write
$\begin{aligned}
& -2 \lambda-2=0 \Rightarrow \lambda=-1 \\
& \therefore \mathrm{P} \equiv(0,-4,4)
\end{aligned}$