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Show that the area of a parallelogram ha...

Show that the area of a parallelogram having diagonals `3 hat i+ hat j-2 hat k\ a n d\ hat i-3 hat j+4 hat k` is `5sqrt(3)` square units.

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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