If for two vectors $\overrightarrow A $ and $\overrightarrow B ,\overrightarrow A \times \overrightarrow B = 0,$ the vectors
If for two vectors $\overrightarrow A $ and $\overrightarrow B ,\overrightarrow A \times \overrightarrow B = 0,$ the vectors
- A
Are perpendicular to each other
- B
Are parallel to each other
- C
Act at an angle of $60^°$
- D
Act at an angle of $30^°$
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- [AIPMT 2005]
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful :
$(a)$ adding any two scalars,
$(b)$ adding a scalar to a vector of the same dimensions ,
$(c)$ multiplying any vector by any scalar,
$(d)$ multiplying any two scalars,
$(e)$ adding any two vectors,
$(f)$ adding a component of a vector to the same vector.
$(a)$ adding any two scalars,
$(b)$ adding a scalar to a vector of the same dimensions ,
$(c)$ multiplying any vector by any scalar,
$(d)$ multiplying any two scalars,
$(e)$ adding any two vectors,
$(f)$ adding a component of a vector to the same vector.
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 $180^{\circ}$
$(C)$ $|A+B|=|A-B|$
$(r)$ $A=B$
$(D)$ $|A \times B|=A B$
$(s)$ 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 |