ï»¿ Show that there is one and only one set of resolved components in a particular direction. from Physics Motion in A Plane Class 11 Manipur Board

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Show that there is one and only one set of resolved components in a particular direction.

Let a given vectorÂ Â be resolved in the direction of two non-parallel vectorsÂ .Â

Let there be two sets of resolved components of resultantÂ Â in the direction ofÂ .Â

That is,Â Â

Since, Â are components ofÂ ,Â

Therefore,

Â

And also,

So, from equations (1) and (2), we have,Â

Since, vector A and B are different non-parallel vectors, so equation (3) is possible only and only if,Â

Hence, both the sets of components are identical. There is one and only one set of resolved components in a particular direction.

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Give three examples of scalar quantities.

Mass, temperature and energy
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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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Give three examples of vector quantities.

Force, impulse and momentum.
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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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