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Show that the asreas of the parallelogra...

Show that the asreas of the parallelogram having diagonals `3hati+hatj-2hastk andhati-3hatj+4hatk is 5sqrt(3)`

Text Solution

Verified by Experts

Let `veca=3hati+hatj-2hatk` and `vecb=veci-3hatj-4hatk`
Then
`vecaxxvecb=|{:(hati,hatj,hatk),(3,1,-2),(1,-3,4):}|=-2hati-14hatj-10hatk`
`rArr |vecaxxvecb|=sqrt((-2)^(2)+(-14)^(2)+(-10)^(2))=sqrt(300)`
`:.` Area of the parallelogram`=(1)/(2)sqrt(300)=5sqrt(3)`
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