Question

The point on the line $\frac{x-2}{1}=\frac{y+3}{-2}=\frac{z+5}{-2}$ at a distance of 6 from the point (2, -3, -5) is

• A. (3, -5, -3)
• B. (4, -7, -9)
• C. (0, 2, -1)
• D. (-3, 5, 3)

Answer 1

The correct option is B (4, -7, -9)

DC’s of the given line is $\frac{1}{3},-\frac{2}{3},-\frac{2}{3}$
Hence, the equation of line can be point in the form $\frac{x-2}{\frac{1}{3}}=\frac{y+3}{\frac{-2}{3}}=\frac{z+5}{\frac{-2}{3}}=r$
$\therefore$ Point is $(2+\frac{r}{3},-3-\frac{2r}{3},-5-\frac{2r}{3})$
$\therefore r=\pm 6$
Points are (4, -7, -9) and (0, 1, -1)