Question

If a, b, c are non-zero vectors such that $\mathbf{a}.\mathbf{b} = \mathbf{a}.\mathbf{c},$ then which statement is true

• A. b = c
• B. $\mathbf{a}\bot(\mathbf{b} - \mathbf{c})$
• C. $\mathbf{b} = \mathbf{c}$ or $\mathbf{a}\bot(\mathbf{b} - \mathbf{c})$
• D. None of these

Answer 1

Answer: (C)

$\mathbf{b} = \mathbf{c}$ or $\mathbf{a}\bot(\mathbf{b} - \mathbf{c})$

Answer 2

$\mathbf{a}.\mathbf{b} = \mathbf{a}.\mathbf{c} \Rightarrow \mathbf{a}.\mathbf{b} - \mathbf{a}.\mathbf{c} = 0 \Rightarrow \mathbf{a}.(\mathbf{b} - \mathbf{c}) = 0$

$\Rightarrow$Either $\mathbf{b} - \mathbf{c} = \mathbf{0}\text{or}\mathbf{a} = \mathbf{0} \Rightarrow \mathbf{b} = \mathbf{c}$ or $\mathbf{a}\bot(\mathbf{b} - \mathbf{c}).$