Chapter 10: Q .9. (page 811)
9. Let be a nonzero vector.
(a) Show that does not necessarily imply that .
(b) What geometric relationship must , , and satisfy if ?
Short Answer
Part a)Proved
Part b)
Chapter 10: Q .9. (page 811)
9. Let be a nonzero vector.
(a) Show that does not necessarily imply that .
(b) What geometric relationship must , , and satisfy if ?
Part a)Proved
Part b)
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Get started for freeIn 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 .)
In Exercises 30–35 compute the indicated quantities when
Suppose that we know the reciprocal rule for limits: If exists and is nonzero, then This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.
What is meant by the triangle determined by vectors u and v in ? How do you find the area of this triangle?
Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is .
(b) True or False: is equal to .
(c) True or False: is equal to .
(d) True or False: is equal to .
(e) True or False: is equal to.
(f) True or False: .
(g) True or False: .
(h) True or False: .
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