Question

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

Answer 1

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It is applicable if angle is obtuse also.

Answer 2

Hii dear,

◆ Proof-
[Refer to the figure]

Consider two vectors OK = a and OM = b.
Let angle between a & b be θ.

In ∆OMN,
sinθ = MN / OM
sinθ = MN / |b|
MN = |b|sinθ

Also,
|a×b| = |a||b|sinθ
|a×b| = OK × MN × 2/2
|a×b| = 2 × A(∆OMK)
A(∆OMK) = 1/2 |a×b|

Thus proved.

Hope that is useful...