Question

If $\hat{i}+\hat{k}$ and $2\hat{i}+\hat{j}+\hat{k}$ are two vectors inclined at an angle $\frac{\pi }{3}$, then the value of $|\overrightarrow{a}+\overrightarrow{b}|$ is.

• A. Grater than 1
• B. Less than 1
• C. Equal to 1
• D. Equal to 0

Answer 1

Answer: (A)

Grater than 1

Given:$\overrightarrow{a}=i+k$ and $\overrightarrow{b}=2i+j+k$. \

Therefore their sum will be $\overrightarrow{a}+\overrightarrow{b}=3i+j+2k$
Hence, $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{3^2+1^2+2^2}$ $=\sqrt{14}$

Thus the $|\overrightarrow{a}+\overrightarrow{b}|$ is greater than $1$