Cross Product

Q.

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, PQ respectively, of a triangle PQR.
$|OX\times OY|=$

1. sin (P+Q)

2. sin (Q + R)

3. sin (P + R)

4. sin 2R

Q.

Let $a=2\hat{i}+\hat{j}-2\hat{k},b=\hat{i}+\hat{j}$ and $c$ be a vector such that $|c-a|=3,|(a\times b)\times c|=3$ and the angle between $c$ and $a\times b$ is ${30}^{\circ }$. Then, $a\cdot c$ is equal to

1. $\frac{25}{8}$

2. 2

3. 5

4. $\frac{1}{8}$