1) Choose two vectors a and b with all components nonzero. Determine the (approximate) angle between them using the dot product. Are your vectors orthogonal? How can you quickly tell using the dot product?
1) Choose two vectors a and b with all components nonzero. Determine the (approximate) angle between them using the dot product. Are your vectors orthogonal? How can you quickly tell using the dot product?
1) Choose two vectors a and b with all components nonzero. Determine the (approximate) angle between them using the dot product. Are your vectors orthogonal? How can you quickly tell using the dot product?
2) Give examples of equations for the following common surfaces: plane, sphere, (elliptic) paraboloid, hyperbolic paraboloid, (circular) cylinder, half cone. For each, which coordinate system(s) are easiest to express the equations?
3) Determine a parameterization for both of the following curves: a line segment connecting two points, and half of a circle centered at the origin.
4) Determine a parameterization for twoof the following common surfaces: plane, sphere, (circular) paraboloid, (circular) cylinder, and half cone.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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