Let PQR be triangle formed by vectors shown in figure.
From figure, the area of is,
Show that:
L.H.S =
Find the area of parallelogram formed by and .
Given,
Here, ,
∴
Now the area of parallelogram formed by vectors is,
Given,
Magitude of cross product is equak to the dot product of two vectors.
i.e.,
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Let PQRS be a parallelogram formed by vectors shown in figure.
From figure, the area of parallelogram PQRS is,
S = PQ. RN
=
Hence the result.