Question

can we define the dot product of two zero vectors?

Answer 1

Dear student

$$\begin{gathered} ThedotProductoftwononzerovectors\overrightarrow{a}and\overrightarrow{b}isgivenby \\ \overrightarrow{a}.\overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta \\ ,where\theta istheanglebetween\overrightarrow{a}and\overrightarrow{b},0\le \theta \le \mathrm{\pi } \\ \mathrm{If}\mathrm{either}\overrightarrow{\mathrm{a}}=0\mathrm{or}\overrightarrow{\mathbf{b}}=0\mathrm{then}\mathrm{\theta }\mathrm{is}\mathrm{not}\mathrm{defined}\mathrm{and}\mathrm{in}\mathrm{this}\mathrm{case}\mathrm{we}\mathrm{define} \\ \overrightarrow{\mathrm{a}.}\overrightarrow{\mathrm{b}}=0 \end{gathered}$$
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