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Class 10 Class 12
Show that if two adjacent sides of a triangle represent the two vectors, then area of the triangle is equal to half of the magnitude of the cross product of two vectors.

Let PQR be triangle formed by vectors  shown in figure.

From figure, the area of  is,

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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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.

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Give three examples of vector quantities.

Force, impulse and momentum.
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What is a vector quantity?

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