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Two adjacent sides of a parallelogram ar...

Two adjacent sides of a parallelogram are respectively by the two vectors `hat(i)+2hat(j)+3hat(k)` and `3hat(i)-2hat(j)+hat(k)`. What is the area of parallelogram?

A

8

B

`8sqrt3`

C

`3sqrt8`

D

192

Text Solution

Verified by Experts

The correct Answer is:
B
Area Of parallelogram `=vecAxxvecB`
`=(hati+2hatj+3hatk)xx(3hati-2hatj+hatk)`
`={:|(hati,hatj,hatk),(1,2,3,),(3,-2,1):}|=(8)hati+(8)hatj-(8)hatk`
Magnitude `=sqrt(64+64+64)=8sqrt(3)`
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