- Home
- Standard 11
- Physics
3-1.Vectors
medium
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.
Option A
Option B
Option C
Option D
Solution
$(a)$ Meaningful : The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
$(b)$ Not Meaningful : The addition of a vector quantity with a scalar quantity is not meaningful.
$(c)$ Meaningful : A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
$(d)$ Meaningful : A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
$(e)$ Meaningful : The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
$(f)$ Meaningful : A component of a vector can be added to the same vector as they both have the same dimensions.
$(b)$ Not Meaningful : The addition of a vector quantity with a scalar quantity is not meaningful.
$(c)$ Meaningful : A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
$(d)$ Meaningful : A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
$(e)$ Meaningful : The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
$(f)$ Meaningful : A component of a vector can be added to the same vector as they both have the same dimensions.
Standard 11
Physics
Similar Questions
Two vectors $A$ and $B$ have equal magnitude $x$. Angle between them is $60^{\circ}$. Then, match the following two columns.
| colum $I$ | colum $II$ |
| $(A)$ $|A+B|$ | $(p)$ $\frac{\sqrt{3}}{2} x$ |
| $(B)$ $|A-B|$ | $(q)$ $x$ |
| $(C)$ $A \cdot B$ | $(r)$ $\sqrt{3} x$ |
| $(D)$ $|A \times B|$ | $(s)$ None |
medium
