ï»¿ Define direction cosines of a vector and show that sum of the square of the direction cosines is equal to unity. from Physics Motion in A Plane Class 11 Manipur Board

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Define direction cosines of a vector and show that sum of the square of the direction cosines is equal to unity.

The cosine of angles made by a vector with the positive directions of X, Y and Z axis is called the direction cosines of a vector.Â

Let us define a vectorÂ , making angleÂ Â respectively with the positive directions of X, Y and Z axis.Â

The direction cosines of vector are,Â

Â

Now, square of magnitude of vector are,Â

Â

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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.Â

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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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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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