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Vector product of three vectors is given...

Vector product of three vectors is given by `vec(A)xx(vec(B)xxvec(C))=vec(B)(vec(A).vec(C))-vec(C)(vec(A).vec(B))`
The value of `hat(i)xx(hat(i)xxhat(j))+hat(j)xx(hat(j)xxhat(k))+hat(k)xx(hat(k)xxhat(i))` is

A

`hat(i)+hat(j)+hat(k)`

B

`-hat(i)-hat(j)-hat(k)`

C

`vec(0)`

D

`-3hat(i)-3hat(j)-3hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Sigmahat(i)xx(hat(i)xxhat(j))=Sigmahat(i)(hat(i).hat(j))-hat(j)(hat(i).hat(i))=-Sigmahat(j)=-(hat(i)+hat(j)+hat(k))`
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