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Q. 4.4 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
Answers (1)
(a) Adding two scalars is meaningful if the two have the same unit or both represent the same physical quantity.
(b) Adding a scalar to a vector of the same dimensions is meaningless as vector quantity has associated direction.
(c) Multiplication of vector with scaler is meaningful as it just increases the magnitude of vector quantity and direction remains the same.
(d) Multiplication of scaler is valid and meaningful, unbounded of any condition. This is because, if we have two different physical quantity then their units will also get multiplied.
(e) Adding two vectors is meaningful if they represent the same physical quantity. This is because their magnitude will get added and direction will remain the same.
(f) Adding a component of a vector to the same vector is meaningful as this represents the same case of adding vectors with the same dimensions. In this, the magnitude of the resultant vector will increase and the direction will remain the same.
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