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
Correct Answer: C
Solution :
\[\mathbf{a}.\mathbf{b}=\mathbf{a}.\mathbf{c}\Rightarrow \mathbf{a}.\mathbf{b}-\mathbf{a}.\mathbf{c}=0\Rightarrow \mathbf{a}.(\mathbf{b}-\mathbf{c})=0\] \[\Rightarrow \]Either \[\mathbf{b}-\mathbf{c}=\mathbf{0}\,\,\text{or}\,\,\mathbf{a}=\mathbf{0}\Rightarrow \mathbf{b}=\mathbf{c}\] or \[\mathbf{a}\bot (\mathbf{b}-\mathbf{c}).\]
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