# A plane containing the point (3, 2, 0) and the line    also contains the point : Option 1) (0, -3, 1) Option 2) (0, 7, 10) Option 3) (0, 7, -10) Option 4) (0, 3, 1)

As we learnt in

Normal form (cartesian form ) -

$lx+my+nz=d$

where d is the distance from origin.

- wherein

$\vec{r}= x\hat{i}+y\hat{j}+z\hat{k}$

$\hat{n}= l\hat{i}+m\hat{j}+n\hat{k}$

putting in $\vec{r}\cdot \hat{n}= d$

We get -  $lx+my+nz= d$

Normal vector of Plane is $=\begin{vmatrix} \hat{i} & \hat{j} &\hat{k} \\ 3-1& 2-2& 0-3\\ 1 & 5 & 4 \end{vmatrix}$

$=\begin{vmatrix} \hat{i} & \hat{j}& \hat{k}\\ 2 & 0& -3\\ 1 & 5 & 4 \end{vmatrix}$$=15\hat{i}-11\hat{j}+10\hat{k}$

15x-11y+10z=23

It passes through (0,7,10)

Option 1)

(0, -3, 1)

This option is incorrect

Option 2)

(0, 7, 10)

This option is correct

Option 3)

(0, 7, -10)

This option is incorrect

Option 4)

(0, 3, 1)

This option is incorrect

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