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The area of the parallelogram whose side...

The area of the parallelogram whose sides are represented by the vector `hat(j)+3hat(k)` and `hat(i)+2hat(j)-hat(k)` is

A

`sqrt(16)sq.unit`

B

`sqrt(59)sq.unit`

C

`sqrt(49)sq.unit`

D

`sqrt(52)sq.unit`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(A)= hat(j)+3hat(k), vec(B)= hat(i)+2hat(j)-hat(k)`
`vec(C )= vec(A)xxvec(B) = |(hati, hatj, hatk), (0, 1, 3), (1, 2, -1)| = -7hat(i)+3hat(j)-hat(k)`
Hence area `=|vec(C )|= sqrt(49+9+1)= sqrt(59) sq.unit`
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