State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:a. adding any two scalarsb. adding a scalar to a vector of the same dimensionsc. multiplying any vector by any scalard. multiplying any two scalarse. adding any two vectorsf. adding a component of a vector to the same vector
Answers
# Answers with explainations-
a) Meaningful.
Its meaningful only if two scalars representing same quantity are added.
b) Not meaningful.
As scalars and vectors must be representing diffrent quantities.
c) Meaningful.
Multiplication of scalar to vector gives rise to new vector quantity.
mass(scalar) × acceleration(vector) = Force(vector)
d) Meaningful.
Multiplying two scalar is always meaningful.
e) Meaningful.
Its meaningful only if two vectors representing same quantity are added.
f) Meaningful.
As component of vector represent same quantity and have same dimensions it can be added to parent vector.
Hope that is useful...
A) Adding any two Scalars :
Two Scalars can be added when their nature is same.
For example two masses can be added but we cannot add a length to mass.
Hence this operation is not meaningful.
B)Adding any two vectors:
This operation is not meaningful as we cannot add vectors of different nature .
Even if two vectors are of same nature we can add them by parallelogram law of vector addition.
C) Adding a scalar to a vector of same dimensions :
This operation is not meaningful
Reason : A vector has a magnitude as well as direction where as scalar has only magnitude but no direction.
d) Adding a component of a vector to the same vectors:
Its not meaningful operation as it vector have different directions.
e) Multiplying any vector by any scalar:
Yes this operation is meaningful
For example mass is scalar and acceleration is vector .
Product of mass and acceleration is a vector quantity.
f) Multiply a scalar quantity:
It is a meaningful operation:
For example length is scalar and breadth is scalar quantity.
Product of two scalars will be a scalar