Angle between Two Planes

Q.

If $OA$is equally inclined to $OX,OY$ and $OZ$ and if $A$is $\sqrt{3}units$ from the origin, then $A$ is

1. $\left(3,3,3\right)$

2. $\left(-1,1,-1\right)$

3. $\left(-1,1,1\right)$

4. $\left(1,1,1\right)$

Q. The angle between the planes $r.(2\hat{i}-\hat{j}+2\hat{k})=3$ and $r.(3\hat{i}-6\hat{j}+2\hat{k})=4$

1. $Co{s}^{-1}\left(\frac{16}{21}\right)$
2. $Si{n}^{-1}\left(\frac{4}{21}\right)$
3. $Co{s}^{-1}\left(\frac{1}{4}\right)$
4. $Co{s}^{-1}\left(\frac{3}{4}\right)$

Q. Let $\sqrt{3}\hat{i}+\hat{j},\hat{i}+\sqrt{3}\hat{j}$ and $\beta \hat{i}+(1-\beta )\hat{j}$ respectively be the position vectors of the points A, B and c with respect to the origin O. if the distance of C from the bisector of the acute angle between OA and OB is $\frac{3}{\sqrt{2}}$, then the sum of all possible values of $\beta$ is

1. $4$
2. $3$
3. $2$
4. $1$