The scalar A ⋅[( B + C ) ×( A + B + C )] equals

Question

The scalar A ⋅[( B + C ) ×( A + B + C )] equals (A) 0 (B) [ A B C ]+[ B C A ] (C) [ A B C ] (D) None of these

Tardigrade Admin · Accepted Answer

A ⋅ ( B + C ) ×( A + B + C ) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2f37ca53e7533d40e08f8272eec4340c-.png" /> [∵ it is a scalar triple product of three vectors of the form A , B + C , A + B + C ] = A ⋅( B × A + B × B + B × C + C × A + C × B + C × C ) = A ⋅( B × A )+ A ⋅( B × C )+ A ⋅( C × B ) =[ A B A ]-[ A B C ]=0

Q. The scalar $A \cdot [(B + C) \times (A + B + C)]$ equals

$0$

$[A B C] + [B C A]$

$[A B C]$

None of these

Q. The scalar A⋅[(B+C)×(A+B+C)] equals

0

[ABC]+[BCA]

[ABC]

None of these

A⋅{(B+C)×(A+B+C)} [∵ it is a scalar triple product of three vectors of the form A,B+C,A+B+C] =A⋅(B×A+B×B +B×C+C×A+C×B+C×C) =A⋅(B×A)+A⋅(B×C)+A⋅(C×B) =[ABA]−[ABC]=0

Q. The scalar $A \cdot [(B + C) \times (A + B + C)]$ equals

$0$

$[A B C] + [B C A]$

$[A B C]$