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Chapter 10: Q 12 (page 848)

Fill in the blanks:
If u and v are nonparallel vectors in $ℝ^{3}$ , then u, v, and $u \times v$ form a ______ triple.

Short Answer

Expert verified

Right - handed

Step by step solution

Given information

If u and v are nonparallel vectors in $ℝ^{3}$

Filling in the blanks

If u and v are nonparallel vectors in $ℝ^{3}$ , then u, v, and $u \times v$ and form aright handedtriple.

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Most popular questions from this chapter

What is meant by the triangle determined by vectors u and v in $ℝ^{3}$ ? How do you find the area of this triangle?

Fill in the blanks to complete each of the following theorem statements:

For $ε > 0, f (x) \in (L - ε, L + ε)$ if and only if $< ε .$

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 $k = 1$ .

(b) True or False: $\sum_{k = 0}^{n} \frac{1}{k + 1} + \sum_{k = 1}^{n} k^{2}$ is equal to $\sum_{k = 0}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(c) True or False: $\sum_{k = 1}^{n} \frac{1}{k + 1} + \sum_{k = 0}^{n} k^{2}$ is equal to $\sum_{k = 1}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(d) True or False: $(\sum_{k = 1}^{n} \frac{1}{k + 1}) (\sum_{k = 1}^{n} k^{2})$ is equal to $\sum_{k = 1}^{n} \frac{k^{2}}{k + 1}$ .

(e) True or False: $\sum_{k = 0}^{m} \sqrt{k} + \sum_{k = m}^{n} \sqrt{k}$ is equal to $\sum_{k = 0}^{n} \sqrt{k}$ .

(f) True or False: $\sum_{k = 0}^{n} a_{k} = - a_{0} - a_{n} + \sum_{k = 1}^{n - 1} a_{k}$ .

(g) True or False: ${(\sum_{k = 1}^{10} a_{k})}^{2} = \sum_{k = 1}^{10} a_{k}^{2}$ .

(h) True or False: $\sum_{k = 1}^{n} {(e^{x})}^{2} = \frac{e^{x} (e^{x} + 1) (2 e^{x} + 1)}{6}$ .

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

$u \times w and w \times u$

Find $u + v a n d u - v$ also sketch $u, v, u + v, u - v$

role="math" localid="1649603943715" $u = (3, 6, 11) a n d v = (1, - 2, 3)$

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Fill in the blanks:If u and v are nonparallel vectors in ℝ3, then u, v, andu×v form a ______ triple.

Short Answer

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Fill in the blanks:
If u and v are nonparallel vectors in $ℝ^{3}$ , then u, v, and $u \times v$ form a ______ triple.