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 Al.
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 .
