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(a) Find and identify the traces of the quadric surface $ x^2 + y^2 - z^2 = 1 $ and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1.(b) If we change the equation in part (a) to $ x^2 - y^2 + z^2 = 1 $, how is the graph affected?(c) What if we change the equation in part (a) to $ x^2 + y^2 + 2y - z^2 = 0 $?

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03:56

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 6

Cylinders and Quadric Surfaces

Vectors

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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01:08

(a) Find and identify the …

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