If the angle between hat{a} and hat{b} is 60^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $\hat{a}$ and $\hat{b}$ are unit vectors,so $|\hat{a}| = 1$ and $|\hat{b}| = 1$.For option $(A)$: $|\frac{\hat{a} + \hat{b}}{\sqrt{3}}|

Vedclass · Accepted Answer

Only $A, C, D$

Vedclass · Answer

(C) Given that $\hat{a}$ and $\hat{b}$ are unit vectors,so $|\hat{a}| = 1$ and $|\hat{b}| = 1$.For option $(A)$: $|\frac{\hat{a} + \hat{b}}{\sqrt{3}}| = \frac{1}{\sqrt{3}} \sqrt{|\hat{a}|^2 + |\hat{b}|^2 + 2|\hat{a}||\hat{b}| \cos 60^{\circ}} = \frac{1}{\sqrt{3}} \sqrt{1 + 1 + 2(1)(1)(0.5)} = \frac{1}{\sqrt{3}} \sqrt{3} = 1$.For option $(B)$: $|\hat{a} + \hat{b}| = \sqrt{1 + 1 + 2(1)(1)(0.5)} = \sqrt{3} 
eq 1$.For option $(C)$: $|\hat{a}| = 1$.For option $(D)$: $|\hat{b}| = 1$.Thus,vectors in $(A), (C),$ and $(D)$ have magnitude one.

If the angle between $\hat{a}$ and $\hat{b}$ is $60^{\circ}$,then which of the following vector$(s)$ have magnitude one?

Similar Questions

If $|\vec{P}+\vec{Q}|=|\vec{P}|=|\vec{Q}|$,then the angle between $\vec{P}$ and $\vec{Q}$ is: (in $^{\circ}$)

If a particle moves from point $P (2, 3, 5)$ to point $Q (3, 4, 5)$,its displacement vector is:

Which of the following is a vector quantity?

The magnitude of a given vector with end points $(4, -4, 0)$ and $(-2, -2, 0)$ is:

Given $A = 3\hat{i} + 4\hat{j}$ and $B = 7\hat{i} + 24\hat{j}$,find a vector that has the same magnitude as $B$ and is parallel to $A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module