The equation of the plane which contains

Question:

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

  1. (1) $x+3 z=10$

  2. (2) $x+3 z=0$

  3. (3) $3 x+z=6$

  4. (4) $3 x-z=0$


Correct Option: , 4

Solution:

$\overrightarrow{\mathrm{n}}=\hat{\mathrm{j}} \times(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$

$=-3 \hat{\mathrm{i}}+0 \hat{\mathrm{j}}+\hat{\mathrm{k}}$

So, $(-3)(x-1)+0(y-2)+(1)(z-3)=0$

$\Rightarrow-3 x+z=0$

Option 4

Alternate :

Required plane is

$\left|\begin{array}{lll}x & y & z \\ 0 & 1 & 0 \\ 1 & 2 & 3\end{array}\right|=0$

$\Rightarrow 3 x-z=0$

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