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Class 10 Class 12

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(b) adding a scalar to a vector of the same dimensions,
(c) multiplying any vector by any scalar,
(d) multiplying any two scalars,
(f) adding a component of a vector to the same vector.

(a)  If the scalars are similar type of quantities, adding of scalars will be meaningful. Scalars of the same dimension can only be added.

(b) Adding a scalar to a vector of the same dimension is meaningless. a scalar cannot be added to a vector.

(c) Any vector can be multiplied by a scalar. A vector when multiplied by a scalar quantity will give us a vector quantity. When the vector quantity acceleration is multiplied by m, we get a force, , which is a meaningful operation.

(d) Two scalars can be multiplied together. For example, when power is multiplied by time t, we get the quatity, work done.

(e) Adding any two vectors is meanigless because two vectors of the same dimnsion can be added.

(f) Adding a component of a vector to the same vector is meaningful. Because both the vectors are of the same dimensions.

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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.

814 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views