If |hat{a} cdot hat{b}| = frac{1}{2},then |ha | vedclass

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

Question

(C) Given that $|\hat{a} \cdot \hat{b}| = \frac{1}{2}$.Since $\hat{a}$ and $\hat{b}$ are unit vectors,$|\hat{a}| = 1$ and $|\hat{b}| = 1$.Thus,$|\cos

Vedclass · Accepted Answer

$1$ or $\sqrt{3}$

Vedclass · Answer

(C) Given that $|\hat{a} \cdot \hat{b}| = \frac{1}{2}$.Since $\hat{a}$ and $\hat{b}$ are unit vectors,$|\hat{a}| = 1$ and $|\hat{b}| = 1$.Thus,$|\cos 	heta| = \frac{1}{2}$,which implies $	heta = 60^\circ$ or $	heta = 120^\circ$.We know that $|\hat{a} - \hat{b}|^2 = |\hat{a}|^2 + |\hat{b}|^2 - 2(\hat{a} \cdot \hat{b})$.Case $1$: If $\hat{a} \cdot \hat{b} = \frac{1}{2}$,then $|\hat{a} - \hat{b}|^2 = 1 + 1 - 2(\frac{1}{2}) = 1$,so $|\hat{a} - \hat{b}| = 1$.Case $2$: If $\hat{a} \cdot \hat{b} = -\frac{1}{2}$,then $|\hat{a} - \hat{b}|^2 = 1 + 1 - 2(-\frac{1}{2}) = 3$,so $|\hat{a} - \hat{b}| = \sqrt{3}$.Therefore,$|\hat{a} - \hat{b}|$ can be $1$ or $\sqrt{3}$.

If $|\hat{a} \cdot \hat{b}| = \frac{1}{2}$,then $|\hat{a} - \hat{b}|$ may be $:-$

Similar Questions

If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other,then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$. The integer value of $n$ is . . . . . . .

If $\overrightarrow{F}=(4 \hat{i}-10 \hat{j}) \text{ N}$ and $\overrightarrow{r}=(-5 \hat{i}-3 \hat{j}) \text{ m}$,then $(\overrightarrow{r} \times \overrightarrow{F})$ is

Find the unit vector perpendicular to the two vectors $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$.

If two vectors $\vec{P} = \hat{i} + 2m \hat{j} + m \hat{k}$ and $\vec{Q} = 4 \hat{i} - 2 \hat{j} + m \hat{k}$ are perpendicular to each other,then the value of $m$ will be:

If $\overrightarrow{A} = (2\hat{i} + 3\hat{j} - \hat{k}) \; m$ and $\overrightarrow{B} = (\hat{i} + 2\hat{j} + 2\hat{k}) \; m$,the magnitude of the component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ will be $...... \; m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module