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The scalar overset(to)(A) .[(overset(to...

The scalar `overset(to)(A) .[(overset(to)(B) xx overset(to)( C)) xx (overset(to)(A) + overset(to)(B) + overset(to)( C))]` equals

A

0

B

`[overset(to)(A)overset(to)(B)overset(to)(C)]+[overset(to)(B)overset(to)(C) overset(to)(A)]`

C

`[overset(to)(A) overset(to)(B) overset(to)(C)]`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(A) ". " {(vec(B) +vec(C )) xx vec(A) + vec(B) + vec(C ))}`
`[:'" it is a scalar triple product of three vectors of the form " vec(A) , vec(B) + vec(C ) , vec(A) + vec(B) +vec(C )]` ,

`=vec(A) ". " (vec(B) xx vec(A) + vec(B) xx vec(B)`
`+vec(B) xx vec(C ) + vec( C) xx vec(A) + vec( C) xx vec(B) + vec( C) xx vec( C))`
`=vec(A) .(vec(B) xx vec(A)) + vec(A).(vec(B) xx vec(C )) + vec(A). (vec(C) xx vec(B))`
`=[vec(A) vec(B) vec(A)] -[vec(A)vec(B) vec(C )]=0`
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