Chapter 10: Q 48. (page 801)
Find a vector in the direction opposite to and with magnitude 3.
Short Answer
The required vector is.
Chapter 10: Q 48. (page 801)
Find a vector in the direction opposite to and with magnitude 3.
The required vector is.
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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.
Consider the sequence of sums
(a) What happens to the terms of this sequence of sums as k gets larger and larger?
(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).
In Exercises 30–35 compute the indicated quantities when
Find the volume of the parallelepiped determined by the vectors u, v, and w.
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.
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