How to prove the triangle area between vectors a and b is 1/2|a × b|

[jbp890]

1. Show that the area of the triangle contained between vector a and vector b and the red line is 1/2 |a x b|

So far i have that bcosO would equal a ...and that 1/2bh should be the area... but I am stuck. can somebody help me prove?

 

[D H]

$b\cos\theta=a$ is not correct. Assuming vector b forms the base of the triangle, $A=1/2bh$ is the correct equation for the area. So what is the height of the triangle? (Hint: it involves only a and theta).