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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
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. 

Let us define a vector straight A with rightwards harpoon with barb upwards on top space equals space A subscript x i with hat on top plus A subscript y j with hat on top plus A subscript z k with hat on top, making angle straight theta subscript straight x comma space straight theta subscript straight y space and space straight theta subscript straight z respectively with the positive directions of X, Y and Z axis. 

The direction cosines of vector are, 

cos space theta subscript x space equals space A subscript x over A semicolon space cos space theta subscript y space equals space A subscript y over A space semicolon space cos theta subscript z space equals space A subscript z over A space
 

Now, square of magnitude of vector are, 

straight A squared space equals space straight A subscript straight x squared space plus space straight A subscript straight y squared space plus space straight A subscript straight z squared space

space space space space space equals space left parenthesis Acosθ subscript straight x right parenthesis squared space plus space left parenthesis Acosθ subscript straight y right parenthesis squared space plus space left parenthesis Acosθ subscript straight z right parenthesis squared space

space space space space space equals space straight A squared left parenthesis cos squared straight theta subscript straight x space plus space cos squared straight theta subscript straight y space plus space cos squared straight theta subscript straight z right parenthesis space

rightwards double arrow space cos squared space straight theta subscript straight x space plus space cos squared straight theta subscript straight y space plus space cos squared straight theta subscript straight z space equals space 1 space


space space space space space space space 

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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

What is a scalar quantity?

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

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