How do the scalar quantities differ from the vector quantities?

How do the scalar quantities differ from the vector quantities?

The only difference between the two quantities is that a scalar quantity includes magnitude only, whereas a vector quantity includes both magnitude as well as direction
Both the quantities include direction and magnitude. Scalar quantities can be combined using the rules of ordinary algebra, whereas vector quantities can be combined using the rules of vector algebra
A scalar quantity includes magnitude only, whereas a vector quantity includes both magnitude and direction, and both the quantities can be combined using the rules of ordinary algebra
A scalar quantity includes magnitude only and scalar quantities can be combined using the rules of ordinary algebra, whereas a vector quantity includes both magnitude and direction, and vector quantities can be combined using the rules of vector algebra
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UPSC Geoscientist – 2022
Option D correctly describes the difference between scalar and vector quantities, including their definitions regarding magnitude and direction, as well as the rules for combining them.
Scalar quantities are physical quantities that have only magnitude (size). Examples include mass, temperature, time, and speed. They can be added, subtracted, multiplied, and divided using the rules of ordinary algebra. Vector quantities are physical quantities that have both magnitude and direction. Examples include displacement, velocity, acceleration, and force. They must be combined using the rules of vector algebra, which take direction into account (e.g., parallelogram law of addition).
Understanding the distinction between scalar and vector quantities is fundamental in physics as it determines how these quantities behave and are manipulated mathematically. The choice of algebra rules (ordinary vs. vector) is a crucial aspect of this distinction.
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