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Chapter 10: Q 12 (page 801)

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.

Short Answer

Expert verified

The required vector is: $<- \frac{a}{2}, - \frac{b}{2}, - \frac{c}{2}>$

Step by step solution

Given information

Given a vector $<a, b, c>$

Finding the vector

The vector is in opposite direction so negative sign has to be applied and half means multiplying the vector with scalar $\frac{1}{2}$ .

The required vector is:

$<- \frac{a}{2}, - \frac{b}{2}, - \frac{c}{2}> .$

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Most popular questions from this chapter

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

If u, v and w are three vectors in $ℝ^{3}$ , what is wrong with the expression $u \times v \times w$ ?

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

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

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

Find the area of the parallelogram determined by the vectors u and v.

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <2, 1, - 5>$

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Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.

Short Answer

Step by step solution

Given information

Finding the vector

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Statistics

Calculus

Probability and Statistics

Discrete Mathematics

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Find a vector parallel to a,b,cbut half as long and pointing in the opposite direction.

Short Answer

Step by step solution

Given information

Finding the vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Statistics

Calculus

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find a vector parallel to $<a, b, c>$ but half as long and pointing in the opposite direction.