3.8 - Multiplying rectangular vectors by a scalar
You can multiply vector quantities by scalar quantities. Let’s say an airplane, as shown
in Concept 1 on the right, travels at a constant velocity represented by the vector (40,
10) m/s. Let's say you know its current position and want to know where it will be if it
travels for two seconds. Time is a scalar. To calculate the displacement, multiply the
velocity vector by the time.
To multiply a vector by a scalar, multiply each component of the vector by the scalar. In
this example, (2 s)(40, 10) m/s = (80, 20) m. This is the plane’s displacement vector
after two seconds of travel.
If you wanted the opposite of this vector, you would multiply by negative one. The result
in this case would be (í40,í10) m/s, representing travel at the same speed, but in the
opposite direction.Multiplying a rectangular vector
by a scalar
Multiply each component by scalar
Positive scalar does not affect directionMultiplying a rectangular vector
by a scalar
sr = (srx,sry)
s = a scalar
r = a vector
rx,ry = r components
What is the displacement d of
the plane after 5.0 seconds?
d = (5.0 s)v
d = (5.0 s) (12 m/s, 15 m/s)
d = ( (5.0 s)(12 m/s), (5.0 s)(15 m/s) )
d = (60, 75) m
(^58) Copyright 2000-2007 Kinetic Books Co. Chapter 03