Chapter 10: Q. 45 (page 790)
Graph the quadric surfaces given by the equations in Exercises 41–48.
The graph of the equation is,
The equation is
We have,
The graph of the above equation is,
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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.
(Hint: Think of the -plane as part of .)
Find the norm of the vector.
Give an example of three vectors in that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.
Find a vector in the direction opposite toandwith magnitude 7.
Prove the first part of Theorem (a): If , then . (Hint: Given , choose . Then show that for it must follow that .)
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