Section 12.7 Cylindrical and Spherical
Coordinates
Recall that in R2, we had two different
coordinate systems rectangular and polar. In
{3, we have discussed rectangular coordinates,
but now we want to discuss two other ways of
describing points and
Section 1 1.1 Curves Defmed by Parametric
Equations
Example: Sketch the curve defmed
parametrically by x : 2 cost, y : r cos 11., over
the interval 0 E r E 227.
Example: Sketch the curve defmed
parametrically by x : r3 2, y : 5 2:, over the
interval 3 E r
12.2 Vectors
Denition: The term vector is used to indicate a
quantity, such as displacement or force, that has
both magnitude AND direction.
Suppose a particle moves along a line segment
from point A to point B, as shown below, while
another partic