   Chapter 12.3, Problem 15E

Chapter
Section
Textbook Problem

# Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)15. a = ⟨4, 3⟩, b = ⟨2. −1⟩

To determine

To find: The angle between vectors a and b vectors.

Explanation

Given:

a=4,3 , and b=2,1 .

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 form 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 two-dimensional vectors.

ab=a1,a2b1,b2

ab=a1b1+a2b2 (2)

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

|a|=a12+a22 (3)

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

|b|=b12+b22 (4)

In equation (2), substitute 4 for a1 , 3 for a2 , 2 for b1 and 1 for b2

### 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

#### Convert the expressions in Exercises 6584 to power form. 8

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 7-22, evaluate the expression. 22. 62.561.961.4

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

#### Evaluate the integral. 20. tan5sec3d

Single Variable Calculus: Early Transcendentals

#### For f(x)=exx,f(x)= a) ex b) xex1x2 c) exxexx2 d) xexxx2

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