Show that the area of the triangle contained between the vectors a and b is one half of the magnitude of a × b.

Question

Philoid · Accepted Answer

Consider two vectors (OK) and (OM) are making angle θ which each other as shown in following figure,

Now,

In ΔOMN we can write the equation,

⇒

We know that magnitude of cross product of vectors a and b is,

= (∵)

= ×OK×MN (∵ = 1)

= 2×Area of ΔOMK

∴ Area of ΔOMK =

Hence Proved.