Question

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

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

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
$\frac{x-2}{\frac{1}{3}}=\frac{y+3}{\frac{-2}{3}}=\frac{z-5}{\frac{-2}{3}}=r\therefore Pointis(2+\frac{r}{3},-3-\frac{2r}{3},-5-\frac{2r}{3})r=\pm 6$
Points are (4, –7, –9) and (0, 1, –1)