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Chapter 10: Q 10 (page 848)

Describe the mathematical expression $u . v$

Short Answer

Expert verified

It represents the dot product of two vectors.

Step by step solution

01

Given information

Mathematical expression $u . v$

02

Describing the mathematical expression

The expression represents the dot product of two vectors.

Let $u = <u_{1}, u_{2}>, v = <v_{1}, v_{2}>, then u . v = u_{1} v_{1} + u_{2} v_{2}$

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Most popular questions from this chapter

Consider the sequence of sums $\frac{1}{3}, \frac{1}{3} + \frac{1}{9}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81}, \dots$

(a) What happens to the terms of this sequence of sums as k gets larger and larger?

(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).

Find a vector in the direction opposite to $<0, - 3, 4>$ and with magnitude 10.

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

Find $\vec{P Q}$ .

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

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.

$P (2, - 5, 1), Q (- 4, 5, 8), R (- 1, - 5, 3)$

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