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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=MNb
MN=bsinθ

a×b=|a|bsinθ
=OK×MN=2×12×OK×MN
=2× Area of OMK

Area of OMK=12×a×b

476743_458297_ans_11d97b3448654b1886aae6147d7247ce.png

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