Motion in A Plane

Physics Part I

Physics

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State and prove that dot product is distributive.

Dot product is distributive. Dot product of a given vector with a sum of number of other vectors is equal to the sum of the dot product of given vector with the other vectors separately.Â

That is,Â Â

Proof: Let us consider that three vectorsÂ Â are represented byÂ respectively.Â

Let, the angle betweenÂ Â isÂ Â and that betweenÂ .Â

Â

In the fig. above, the resultant vector is given byÂ .Â Â is the resultant ofÂ .Â

Angle made byÂ .

Construction: From P and T draw perpendiculars PM and TN on OL and draw perpendicular PS from P on TN.Â

Â

Hence, from the above result we can see that the dot product is distributive.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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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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