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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12

What are the characteristics of dot product?


The characteristics of dot product are: 

(i)  Dot product of two vectors is commutative.

Mathematically,   straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space straight B with rightwards arrow on top times straight A with rightwards arrow on top 

(ii)  Dot product is distributive. 

Mathematically,  straight A with rightwards arrow on top times left parenthesis straight B with rightwards arrow on top plus straight C with rightwards arrow on top right parenthesis space equals space straight A with rightwards arrow on top times space straight B with rightwards arrow on top space plus space straight A with rightwards arrow on top times straight C with rightwards arrow on top 

(iii) Dot product of two perpendiculars vectors is zero.

Mathematically  straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space 0            if   straight A with rightwards arrow on top space perpendicular space straight B with rightwards arrow on top 

(iv) Dot product of vector with itself is equal to square of magnitude of vector. 

Mathematically,    straight A with rightwards arrow on top times straight A with rightwards arrow on top space equals space straight A squared

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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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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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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 vector quantities.

Force, impulse and momentum.
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