Question

What do vectors and scalars have in common? How do they differ?

Short answer

The similarity between vectors and scalars is that both have magnitudes with units. The difference between vectors and scalars is that vectors have direction, but scalars don’t, and the resultant of two vector quantities can be zero under certain conditions, but two scalars can never add up to zero.

Step-by-step solution

Physical quantity

The physical property of a material such as its mass, length, etc., that can be quantified is known as a physical quantity.It can be expressed as a numerical value and a unit.

A physical quantity is classified further as either a vector or a scalar quantity.

Similarity between a vector and a scalar  

Both vector and scalar quantities have numerical values (magnitudes) and units.

Difference between a vector and a scalar

A vector quantity possesses both magnitude with unit and direction, but a scalar quantity only has magnitude with unit.

The vector quantities can be added or subtracted according to the vector law of addition; so, the resultant of two vector quantities can be zero under certain conditions, but scalar quantities can only be added or subtracted with ordinary algebraic laws, so two scalar quantities can never add up to zero.

Hence, the difference between vectors and scalars is that vectors have direction, but scalars don’t, and the resultant of two vector quantities can be zero under certain conditions, but two scalars can never add up to zero.