   Chapter 12.3, Problem 17E

Chapter
Section
Textbook Problem

# Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)17. a = ⟨1, −4, 1⟩, b = ⟨0, 2, −2⟩

To determine

To find: The angle between vectors a and b .

Explanation

Given:

a=1,4,1 , b=0,2,2 .

Formula:

Write the expression to find ab in terms of θ .

ab=|a||b|cosθ

Here,

|a| is the magnitude of a vector,

|b| is the magnitude of b vector, and

θ is the angle between vectors a and b.

Rearrange the equation.

cosθ=ab|a||b|

θ=cos1(ab|a||b|) (1)

A minimum of two vectors are required to perform a dot product. The resultant dot product of two vectors is scalar. So, the dot product is also known as a scalar product.

Consider a general expression to find the dot product between two three-dimensional vectors.

ab=a1,a2,a2b1,b2,b2

ab=a1b1+a2b2+a3b3 (2)

Consider a general expression to find the magnitude of a three-dimensional vector; that is a=a1,a2,a3 .

|a|=a12+a22+a32 (3)

Similarly, consider a general expression to find the magnitude of a three-dimensional vector that is b=b1,b2,b3 .

|b|=b12+b22+b32 (4)

In equation (2), substitute 1 for a1 , –4 for a2 , 1 for a3 , 0 for b1 , 2 for b2 and –2 for b3

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 7-10, solve for x or y. (3x)2+(74)2=45

Calculus: An Applied Approach (MindTap Course List)

#### In Exercises 7-10, find the slope of the line shown in each figure. 9.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: converges mean exists.

Study Guide for Stewart's Multivariable Calculus, 8th

#### Using differentials, an approximation to (3.04)3 is: 28.094464 28.08 28.04 28

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 