Question

If $a$ and $b$ are two unit vectors inclined at an angle $\frac {\pi}{3}$, then the value of $|a + b|$ is

• A. greater than 1
• B. less than 1
• C. equal to 1
• D. equal to 0

Answer 1

Answer: (A)

Given, $| a |=| b |=1$ and $\theta=\pi / 3$
Now, $| a + b |^{2} =| a |^{2}+| b |^{2}+2| a || b | \cos \theta$
$=1^{2}+1^{2}+2 \times 1 \times 1 \times \cos \frac{\pi}{3}$
$=1+1+2 \times \frac{1}{2}=1+1+1=3$
$\therefore | a + b | =\sqrt{3}$
$\therefore | a + b | > 1$