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Mathematical Methods — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsMathematical Methods4 Marks
Question
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful.
i. Adding any two scalars,
ii. Adding a scalar to a vector of the same dimensions,
iii. Multiplying any vector by any scalar,
iv. Multiplying any two scalars,
v. Adding any two vectors. (NCERT)
✓

Answer

  1. Not any two scalars can be added. To add two scalars it is essential that they represent same physical quantity.
  2. This operation is meaningless. Only a vector can be added to another vector.
  3. This operation is possible. When a vector is multiplied with a dimensional scalar, the resultant vector will have different dimensions.
    eg.: acceleration vector is multiplied with mass (a dimensional scalar), the resultant vector has the dimensions of force.
    When a vector is multiplied with non – dimensional scalar, it will be a vector having dimensions as that of the given vector.
    eg.:$\overrightarrow{ A } \times 3=3 \overrightarrow{ A }$
  4. This operation is possible. Multiplication of non-dimensional scalars is simply algebraic multiplication. Multiplication of non dimensional scalars will result into scalar with different dimensions.
    eg.: Volume × density = mass.
  5. Not any two vectors can be added. To add two vectors it is essential that they represent same physical quantity.

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