Show that the area of the triangle contained between the vector `overset rarr(r ) and overset rarr(b)` is one half of the magnitude of `overset rarr(a) xx overset rarr(b)`

Explanation

Let `oversetrarr(a)` be represented by `overset rarr (OP)` and `overset rarr (b)` be represented by `overset rarr (OQ)` Let `/_POQ = theta`, Fig. Complete the `|| gm OPRQ`. Join `PQ`.
Draw `QN_|_ OP`
In `Delta OQN, sin theta = (QN)/(OQ) = (QN)/(b)`
`QN = b sin theta`
now, by defination, `|overset rarr(a) xx overset rarr(b)| = ab sin theta = (OP)(QN) = (2(OP)(QN))/(2) = 2 xx` area of `Delta OPQ`
`:.` area of `Delta = (1)/(2) |overset rarr(a) xx overset rarr(b)|`, which was to be proved.