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A vector of magnitude 6m points _{} north of east. A second vector whose magnitude is 8m points
_{} west of south. If we add these two vectors together, what
is the resultant?

Given: Vector
1 magnitude = 6m, direction = _{} north of east

Vector
2 magnitude = 8m, direction = _{} west of south

Unknown: Vector that results from adding these two, that is the magnitude and direction of the resultant vector.

Physical (mathematical) Principles and Ideas: rules for adding vectors

Solution: Our sketch tells us that the two
vectors lie on the same line, but point in opposite directions. That means we will actually be subtracting
one of these vectors from the other. It
is a little easier to subtract the smaller one from the larger, i.e., 8m – 6m =
2m. Now we know the magnitude of our
resultant. By setting the subtraction
up this way, what we have actually done is to make the 60^{o} west of
south (which is, of course, the same as 30^{o} south of west) direction
positive and the 30^{o} north of east direction negative. Since our value above is +2m, we know the
direction is 60^{o} west of south.
(What value would indicate a direction of 30^{o} north of east
if 60^{o} west of south is positive?)

All vector problems involving vectors that lie on a line are worked similarly. Among the vector quantities we work with in physics are: displacement, velocity, acceleration, force, momentum, and electric and magnetic fields.

Other Kinematics Examples: 1 2 3 4 5 6 7 8 9 10

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