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| Multiplication of Vectors by Real Numbers, i.e., 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 Al. |
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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 .
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| 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. |
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| 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 . |
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| Example |
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 The multiplication of velocity vector by time (a scalar) gives us displacement. |
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 The multiplication of velocity vector by mass (a scalar) gives us momentum. |
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