Question

The equation of the plane which contains the $y-$ axis and passes through the point $(1,2,3)$ is:

• A. $3x+z=6$
• B. $3x-z=0$
• C. $x+3z=10$
• D. $x+3z=0$

Answer 1

The correct option is B $3x-z=0$

Let $A=(1,2,3)$ and $O$ be the origin
D.R.'s of $y-$ axis are $0,1,0$
$\overrightarrow{OA}=(1,2,3)$
Therefore, the required equation of the plane
$\left|\begin{array}{ccc}x& y& z\\ 0& 1& 0\\ 1& 2& 3\end{array}\right|=0\Rightarrow 3x-z=0$