If $a \cdot b = 0$,then:

Let the position vectors of the points $P, Q, R$ and $S$ be $\vec{a}=\hat{i}+2 \hat{j}-5 \hat{k}$,$\vec{b}=3 \hat{i}+6 \hat{j}+3 \hat{k}$,$\vec{c}=\frac{17}{5} \hat{i}+\frac{16}{5} \hat{j}+7 \hat{k}$ and $\vec{d}=2 \hat{i}+\hat{j}+\hat{k}$,respectively. Then which of the following statements is true?

The orthogonal projection vector of $\vec{a} = 2\hat{i} + 3\hat{j} + 3\hat{k}$ on $\vec{b} = \hat{i} - 2\hat{j} + \hat{k}$ is

If $l\vec{a} + m\vec{b} + n\vec{c} = \vec{0},$ where $l, m, n$ are scalars and $\vec{a}, \vec{b}, \vec{c}$ are mutually perpendicular non-zero vectors,then

If $ABCD$ is a cyclic quadrilateral with $R$ as the radius of the circumcircle and $(AB)^2+(CD)^2=4R^2$,then:

Let $a = 2\hat{i} - \hat{j} + 2\hat{k}$ and $b = 3\hat{i} - 2\hat{j} - 5\hat{k}$ be two vectors. Then the projection vector of $b$ on a vector perpendicular to $a$ is