A) \[3{{r}^{2}}\]
B) \[{{r}^{2}}\]
C) 0
D) None of these
Correct Answer: B
Solution :
Let \[\mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\]\[\Rightarrow \mathbf{r}\,.\,\mathbf{i}=x,\] \[\mathbf{r}\,.\,\mathbf{j}=y,\] \[\mathbf{r}\,.\,\mathbf{k}=z\] \[\Rightarrow {{(\mathbf{r}\,.\,\mathbf{i})}^{2}}+{{(\mathbf{r}\,.\,\mathbf{j})}^{2}}+{{(\mathbf{r}\,.\,\mathbf{k})}^{2}}={{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{r}^{2}}.\]
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