Question

If O is the origin and the coordinates of A and B are $(51,65)$ and $(75,81)$ respectively. Then $OA\times OB\cos \angle AOB$ is equal to

Answer 1

From distance fromula,

$(OA{)}^2=(51{)}^2+(65{)}^2$, $(OB{)}^2=(75{)}^2+(81{)}^2$

$(AB{)}^2=(75-51{)}^2+(81-65{)}^2$
And from $△OAB,$
$(AB{)}^2=(OA{)}^2+(OB{)}^2-2OA\times OB\cos \angle AOB$
$\Rightarrow 2OA\times OB\cos \angle AOB=2(75\times 51+81\times 65)$
$\Rightarrow OA\times OB\cos \angle AOB=3825+5265=9090$