Question

State the whether given statement is true or false

$\overrightarrow{a}=5\hat{i}-\hat{j}-3\hat{k}$ and $\overrightarrow{b}=\hat{i}+3\hat{j}-5\hat{k}$ then show that the vectors $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ are perpendicular

• A. True
• B. False

Answer 1

The correct option is A True

$\underset{a}{\to }=5\hat{i}-1\hat{j}-3\hat{k}$ and

$\underset{b}{\to }=1\hat{i}+3\hat{j}-5\hat{k}$

$\underset{a}{\to }+\underset{b}{\to }=6\hat{i}+2\hat{j}-8\hat{k}$

$\underset{a}{\to }-\underset{b}{\to }=4\hat{i}-4\hat{j}+2\hat{k}$

taking their dot product,

$(\underset{a}{\to }+\underset{b}{\to }).(\underset{a}{\to }-\underset{b}{\to })=24-8-16=0$

hence $(\underset{a}{\to }+\underset{b}{\to })and(\underset{a}{\to }-\underset{b}{\to })$ are perpendicular.