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

#### Consider two vectors OK = vector |a|and OM = vector|b|, inclined at an angle θ as shown in the following figure.

In △OMN, we can write the relation:

sinθ=MNOM=MN∣∣→b∣∣

⟹MN=∣∣→b∣∣sinθ

∣∣→a×→b∣∣=|→a|∣∣→b∣∣sinθ

=OK×MN=2×12×OK×MN

=2× Area of △OMK

⟹ Area of △ OMK=12×∣∣→a×→b∣∣