Question

The points $A(\mathbf{a}),B(\mathbf{b}),C(\mathbf{c})$ will be collinear if

• A. $\mathbf{a} + \mathbf{b} + \mathbf{c} = \mathbf{0}$
• B. $\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a} = \mathbf{0}$
• C. $\mathbf{a}.\mathbf{b} + \mathbf{b}.\mathbf{c} + \mathbf{c}.\mathbf{a} = 0$
• D. None of these

Answer 1

Answer: (B)

$\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a} = \mathbf{0}$

Answer 2

$(\mathbf{b} - \mathbf{a}) \times (\mathbf{c} - \mathbf{b}) = 0$ or $\mathbf{b} \times \mathbf{c} + \mathbf{a} \times \mathbf{b} + \mathbf{c} \times \mathbf{a} = \mathbf{0}$.