Q67 / 150 · MHT CET 2021 (24 Sep Shift 2) · Mathematics
The co-ordinates of the points on the line $\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$ at a distance of 12 units from the point $\mathrm{A}(-2,1,-1)$ are
- Correct answerA$(2,9,-9),(-6,-7,7)$
- B$(2,9,7),(6,5,-9)$
- C$(6,9,-5),(-10,9,-5)$
- D$(6,-7,3),(-10,9,3)$
Solution
$\frac{\mathrm{x}+2}{1}=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}+1}{-2}=\lambda \quad \ldots$ (say)
Hence coordinates of any point on the given line are $(\lambda-2,2 \lambda+1,-2 \lambda-1)$.
This point is at a distance of 12 units from $(-2,1,-1)$.
$\begin{array}{ll}
\therefore \quad & 12=\sqrt{(\lambda-2+2)^2+(2 \lambda+1-1)^2+(-2 \lambda-1+1)^2} \\
& =\sqrt{\lambda^2+4 \lambda^2+4 \lambda^2}=3 \lambda \\
\therefore & \lambda= \pm 4 \Rightarrow \text { Required point }=(2,9,-9) \text { or }(-6,-7,7)
\end{array}$
Hence, the correct answer is option: 'A'.