Paragraph: Let O be the origin, and O X , O Y , O Z be three unit...

$\overset{\to}{OX}, \overset{\to}{OY}, \overset{\to}{OZ}$ are unit vectors in the directions of sides $\overset{\to}{OR}, \overset{\to}{RP}$ and $\overset{\to}{PQ}$ respectively,

$∴ \overset{\to}{OX} = \overset{\to}{QR}\left|\overset{\to}{QR}\right|, \overset{\to}{OY} = \overset{\to}{RP}\left|\overset{\to}{RP}\right|, \overset{\to}{OZ} = \overset{\to}{PQ}\left|\overset{\to}{PQ}\right|$

$∴ \left|\overset{\to}{OX} \times \overset{\to}{OY}\right| = \dfrac{\left|\overset{\to}{OR} \times \overset{\to}{RP}\right|}{\left|\overset{\to}{QR}\right|\left|\overset{\to}{RP}\right|}$

$= \dfrac{\left|\overset{\to}{QR}\right|\left|\overset{\to}{RP}\right|\sin \left(P + Q\right)}{\left|\overset{\to}{QR}\right|\left|\overset{\to}{RP}\right|}$

$= \sin \left(P + Q\right)$