For three vectors, `vecu, vecv and vecw` which of the following expressions is not equal to any of the remaining three ?

Options

A. `vecu.(vecvxxvecw)`
B. `(vecuxxvecw).vecu`
C. `vecv.(vecuxxvecw)`
D. `(vecuxxvecv).vecw`

Answer

C

Explanation

We have
`vecu.(vecvxxvecw)=(vecvxxvecw).vecu` [ `:'` Dot product is commutative]
So, expression in options a and b are equal .
Since the position of dot cross can be interchanged in scalar triple product. Therefore,
`(vecuxxvecv).vecw=vecu.(vecvxxvecw)`
So expression in options a and d are equal.
But `vecv.(vecuxxvecw)=(vecuxxvecw).vecv=vecu.(vecwxxvecv)=-vecu.(veccxxvecw)`
Hence expression in c is not equal to he remaining three.