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Show that the area of the triangle conta...

Show that the area of the triangle contained between the vectors `veca` and `vecb` is one half of the magnitude of `veca xx vecb`.

Text Solution

Verified by Experts

Let `vec(OP) and vec(OQ)` represents vectors `vecaand vecb` and `anglePOQ=theta`
In parallelogram OPRO, draw `QS botOP`
In `DeltaOQS , sin theta=(QS)/(OQ)implies sin theta =(QS)/b=QS = b sin theta`
We know `|vecaxxvecb|=ab sin theta=(2(OP)(QS))/(2)`
`|vecaxxvecb|=2xx"area" (DeltaOPQ)`
Therefore, are of `DeltaOPQ=1/2|vecaxxvecb|`
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