Question

The coordinates of a point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point (1, –1, 0) nearer the origin are

• A. $(9,–13,4)$
• B. $\left(8\sqrt{14,-12,-1}\right)$
• C. $(-8\sqrt{14,12,-1})$
• D. $(-7,11,-4)$

Answer 1

The correct option is D $(-7,11,-4)$

Any point on given line is (2r + 1, –3r – 1, r) its distance from (1, –1, 0).
$\Rightarrow (2r{)}^2+(-3r{)}^2+r^2=(4\sqrt{14}{)}^2\Rightarrow r=\pm 4\Rightarrow$ Coordinates are (9, –13, 4) and (–7, 11, –4) and nearer to the origin is (–7, 11, –4)