Question

If a line is given by $\frac{x-2}{3}=\frac{y+10}{5}=\frac{z+6}{2}$, then which of the following points lies on this line?

• A. $(5,11,0)$
• B. $(3,10,0)$
• C. $(11,5,0)$
• D. $(0,5,11)$

Answer 1

The correct option is C $(11,5,0)$

Putting $x=11$ and $y=5$ and $z=0$ in the given equation of line, we get

$\begin{array}{c}\frac{x-2}{3}=\frac{y+10}{5}=\frac{z+6}{2}\\ \frac{11-2}{3}=\frac{5+10}{5}=\frac{0+6}{2}\\ \frac{9}{3}=\frac{15}{3}=\frac{6}{2}\\ 3=3=3\end{array}$

therefore $(11,5,0)$ satisfies given equation of line

hence $(11,5,0)$ lies on the given line

Option $C$ is the correct answer.