Supoose that a=0.If a b=a c then is b=c ? - Vidyadip

Question

Supoose that $\bar{a}=0$.If $\bar{a} \cdot \bar{b}=\bar{a} \cdot \bar{c}$ then is $\bar{b}=\bar{c}$ ?

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Answer

No. Take $\bar{b}=\hat{i}, \bar{c}=\hat{j}$.

Then $\bar{a} \cdot \bar{b}=\bar{a} \cdot \bar{c}=0$, but $\bar{b} \neq \bar{c}$

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