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}. $