Vector Algebra Question 374

Question: $ {{(\mathbf{r},.,\mathbf{i})}^{2}}+{{(\mathbf{r},.,\mathbf{j})}^{2}}+{{(\mathbf{r},.,\mathbf{k})}^{2}}= $

Options:

A) $ 3r^{2} $

B) $ r^{2} $

C) 0

D) None of these

Show Answer

Answer:

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}. $