Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$
- A$\frac{{2\hat i + \hat j + 4\hat k}}{{\sqrt {21} }}$
- B$\frac{{ - 2\hat i + \hat j + 4\hat k}}{{\sqrt {21} }}$
- C$\frac{{ - 2\hat i - \hat j + 4\hat k}}{{\sqrt {21} }}$
- D$\frac{{2\hat i + \hat j + 4\hat k}}{{\sqrt 5 }}$
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If $\theta$ is the angle between two vectors $A$ and $B$, then match the following two columns.
colum $I$
colum $II$
$(A)$ $A \cdot B =| A \times B |$
$(p)$ $\theta=90^{\circ}$
$(B)$ $A \cdot B = B ^2$
$(q)$ $\theta=0^{\circ}$ or $180^{\circ}$
$(C)$ $|A+B|=|A-B|$
$(r)$ $A=B$
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$(s)$ None
| colum $I$ | colum $II$ |
| $(A)$ $A \cdot B =| A \times B |$ | $(p)$ $\theta=90^{\circ}$ |
| $(B)$ $A \cdot B = B ^2$ | $(q)$ $\theta=0^{\circ}$ or $180^{\circ}$ |
| $(C)$ $|A+B|=|A-B|$ | $(r)$ $A=B$ |
| $(D)$ $|A \times B|=A B$ | $(s)$ None |
Find the angle between two vectors with the help of scalar product.
Find the angle between two vectors with the help of scalar product.