Question

If a and b are two vectors such that a . b = 0 and $\mathbf{a} \times \mathbf{b} = \mathbf{0},$ then

• A. a is parallel to b
• B. a is perpendicular to b
• C. Either a or b is a null vector
• D. None of these

Answer 1

Answer: (C)

Either a or b is a null vector

Answer 2

$\mathbf{a}.\mathbf{b} = 0 \Rightarrow \mathbf{a}\bot\mathbf{b}$ or $\mathbf{a} = \mathbf{0}$or $\mathbf{b} = \mathbf{0}$

and $\mathbf{a} \times \mathbf{b} = \mathbf{0} \Rightarrow \mathbf{a}||\mathbf{b}$ or $\mathbf{a} = \mathbf{0}$ or $\mathbf{b} = \mathbf{0}$

Hence, either $\mathbf{a}$or $\mathbf{b}$ is a null vector.