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Class 10 Class 12
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.

That is,

Proof: Let us consider that three vectors  are represented by respectively.

Let, the angle between  is  and that between

In the fig. above, the resultant vector is given by  is the resultant of

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

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

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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

What is a scalar quantity?

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

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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Give three examples of scalar quantities.

Mass, temperature and energy
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