question_answer

For any vectors a, b, c  \[\mathbf{a}\times (\mathbf{b}+\mathbf{c})+\mathbf{b}\times (\mathbf{c}+\mathbf{a})+\mathbf{c}\times (\mathbf{a}+\mathbf{b})=\] [Roorkee 1981; Kerala (Engg.) 2002]

A)                 0

B)                 \[\mathbf{a}+\mathbf{b}+\mathbf{c}\]

C)                 \[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\]

D)                 \[\mathbf{a}\times \mathbf{b}\times \mathbf{c}\]