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Chapter 10: Q 17 (page 848)

Fill in the blanks and give the name of the property.
For any three vectors u, v and w, $u . (v + w) =______$

Short Answer

Expert verified

The required expression is: $u . (v + w) = u . v + u . w$ ; Distributive property

Step by step solution

Given information

Any three vectors u, v and w.

Completing the expression

The complete expression may be written as:

$u . (v + w) = u . v + u . w$

It is an example of distributive property.

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Most popular questions from this chapter

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.

$P (3, 1, 8), Q (0, 6, - 1), R (- 3, 5, - 3)$

For each function f and value x = c in Exercises 35–44, use a sequence of approximations to estimate $f^{'} (c)$ . Illustrate your work with an appropriate sequence of graphs of secant lines.

role="math" localid="1648705352169" $f (x) = e^{x}, c = 0$

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

Find the norm of the vector. $v = (\frac{1}{2}, \frac{1}{3}, \frac{1}{4})$

Use the definition of the derivative to find $f'$ for each function $f$ in Exercises 39-54

$f (x) = \frac{1}{\sqrt{2 x + 1}}$

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Fill in the blanks and give the name of the property.For any three vectors u, v and w,u.(v+w)=______

Short Answer

Step by step solution

Given information

Completing the expression

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Most popular questions from this chapter

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Fill in the blanks and give the name of the property.
For any three vectors u, v and w, $u . (v + w) =______$