端木·宇 2008-6-19 20:26
Multiplication by a Scalar
Multiplication is like repeated addition. Multiplying 4 by 3 means adding four three times: [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/c31ae837ba747538be6e985fc9280119.gif[/img]. The multiplication of a vector times a scalar works in the same way. Multiplying the vector [i][b]A[/b][/i] by the positive scalar [i]c[/i] is equivalent to adding together [i]c[/i] copies of the vector [i][b]A[/b][/i]. Thus 3[i][b]A[/b][/i] = [i][b]A[/b][/i] + [i][b]A[/b][/i] + [i][b]A[/b][/i]. Multiplying a vector by a scalar will get you a vector with the same direction, but different magnitude, as the original.
[align=center][img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/cbbf5137964262d8aeceb3079a67eeee.gif[/img][/align]
The result of multiplying [i][b]A[/b][/i] by [i]c[/i] is a vector in the same direction as [i][b]A[/b][/i], with a magnitude of [img]http://www.24en.com/d/file/sat/sat2/physics/2008-01-24/ca703e5c2d574e5e4acb9977dc7ebc74.gif[/img]. If [i]c[/i] is negative, then the direction of [i][b]A[/b][/i] is reversed by scalar multiplication.
