Chapter 10: Q. 48 (page 790)
Graph the quadric surfaces given by the equations in Exercises 41–48.
The graph is,
The given equation is
We have,
The graph of the above equation is shown below,
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Find a vector in the direction opposite toandwith magnitude 7.
Use the Intermediate Value Theorem to prove that every cubic function has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.
In Exercises 37–42, find and find the unit vector in the direction of v.
In Exercises 36–41 use the given sets of points to find:
(a) A nonzero vector N perpendicular to the plane determined by the points.
(b) Two unit vectors perpendicular to the plane determined by the points.
(c) The area of the triangle determined by the points.
What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v and w? How do you find the volume of the parallelepiped determined by u, v and w?
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