Question

If the vectors $\mathbf{a},\mathbf{b}$ and c are represented by the sides $BC,CA$ and $AB$ respectively of the $\Delta ABC$, then

• A. $\mathbf{a}.\mathbf{b} + \mathbf{b}.\mathbf{c} + \mathbf{c}.\mathbf{a} = 0$
• B. $\mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} = \mathbf{c} \times \mathbf{a}$
• C. $\mathbf{a}.\mathbf{b} = \mathbf{b}.\mathbf{c} = \mathbf{c}.\mathbf{a}$
• D. $\mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} = \mathbf{c} \times \mathbf{a} = 0$

Answer 1

Answer: (B)

$\mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} = \mathbf{c} \times \mathbf{a}$

Answer 2

Here $a + b + c = 0$. Take cross products with a and b by turn.