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Chapter 10: Q 3 TB (page 800)

Provide definition of Distributive property of multiplication over addition for real numbers.

Short Answer

Expert verified

While multiplying a real number with sum of real numbers, the multiplication gets distributed over addition.

Step by step solution

01

Given information

Real numbers

02

Defining the property

When the sum of real numbers is multiplied with another real number, the multiplication gets distributed over addition.

Let $a, b, c$ be three real numbers.

As per the distributive property of multiplication over addition:

$a * (b + c) = a * b + a * c$

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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.

(c) The area of the triangle determined by the points.

$P (1, 6), Q (0, - 3), R (- 5, 4)$

(Hint: Think of the $x y$ -plane as part of $ℝ^{3}$ .)

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

role="math" localid="1649400253452" $(u \times v) \times w and u \times (v \times w)$

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 the mass of a 30-centimeter rod with square cross sections of side length 2 centimeters, given that the density of the rod x centimeters from the left end is ρ(x) = $10 \cdot 5 + 0 \cdot 01527 x^{2}$ grams per cubic centimeter.

Find $\vec{P Q}$ .

$P = (3, 6), Q = (- 3, - 2)$

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