Chapter 10: Q 20 (page 848)
Fill in the blanks and give the name of the property.
u, v, and w be vectors in . Then
Short Answer
The required expression is; Distributive property
Chapter 10: Q 20 (page 848)
Fill in the blanks and give the name of the property.
u, v, and w be vectors in . Then
The required expression is; Distributive property
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Get started for freeIf u and v are vectors in such that , what can we conclude about u and 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.
(Hint: Think of the -plane as part of .)
In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.
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: .
What is meant by the parallelogram determined by vectors u and v in ? How do you find the area of this parallelogram?
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