Scalar Multiple of a Vector

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The multiplication of a vector by a real number assumes a lot of significance in such statements as - velocity of car B is double the velocity of car A^l.

When a vector is multiplied by a real number, say l, then we get another vector l.  The magnitude of  l is l times the magnitude of . If l is positive, then the direction of  l  is the same as that of . If l is negative, then the direction of lis opposite to that of .

If is multiplied by zero, we get a vector whose magnitude is zero and whose direction is arbitrary. This vector is called a zero vector or null vector.

If l is a pure number and has no units, then the units of lare the same as those of . But, if the scalar has a certain unit, then the unit of l will be different from that of .

Example

• The multiplication of velocity vector by time (a scalar) gives us displacement.

• The multiplication of velocity vector by mass (a scalar) gives us momentum.