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Question

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

Solution
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#### 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∣∣

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