Question

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

• A. $(9,-13,-4)$
• B. $(8\sqrt{14,}-12,-1)$
• 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).