Question 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.
Chapter Motion In A Plane Page 85
Answers
(B) naah !! Its not possible , because vector can be added with vector quantity.
(C) yeah !! this is possible. When a scalar multiply with a vector we get a vector quantity which direction depends upon sign of scalar quantity .
(D) yes !! Its true . Example : mass = volume x density
We know, volume and density both are scalar quantities and mass is product of it .
Hence multiplication of two scalar quantity must be scalar quantity.
(E) No , it's not a meaningful . because only vectors having same dimensions and unit can be added.
(F) yeah ! It's meaningful . we can be added component of vector to same vector. Due to both have same dimensions.
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a) Meaningful
b) Not Meaningful
c) Meaningful
d) Meaningful
e) Meaningful
f) Meaningful
Explanation:
(a) The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
(b) The addition of a vector quantity with a scalar quantity is not meaningful.
(c) A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
(d) A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
(e) The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
(f) A component of a vector can be added to the same vector as they both have the same dimensions.
I hope, this will help you
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