Problem

Find the angle between the vectors. (First find a…

View

Question

Answered step-by-step

Problem 15 Easy Difficulty

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)

$ a = \langle 4, 3 \rangle , b = \langle 2, -1 \rangle $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Jacquelyn Trost

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Top Calculus 3 Educators

Watch More Solved Questions in Chapter 12

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Video Transcript

for this problem. We have been given two vectors A and B, and we want to find the angle between these two vectors. We're going to find it first, is an exact number and then approximated to the nearest degree. Now we have a the're, um that tells us how we how the angle between two vectors is related to the vectors themselves. Our formula says that the co sign of fate a fate of being the angle between A and B the co sign of that angle is the dot product of our two vectors over the multiplication of the magnitude of those two vectors. Okay, so we dot product on top, and then we multiply the magnitudes on the bottom. So let's see what we have. Let's find our pieces first of all dot product For the dot product, we multiply the X co uh, the X pieces together, and then we add the multiplication of the white pieces. So for this particular case, are dot product is going to be eight plus negative three or five. Now, let's look at the magnitudes over magnitude of we're just finding the distance that the that distance along my vector so that's going to be using, um, kind of kind things. This Pythagorean theorem. Okay, I've got four squared plus three squared that's gonna give me 25. So the magnitude of Vector A is five. How about the magnitude of Vector be against square root? We're gonna take our first coordinate squared, plus our second coordinate squared. That's going to give me the square root of five. So now I have all of the pieces. Let's put this into our formula. Co sign of theta equals the dot product, which in this case is five over the magnitude of the first times the magnitude of the second. Those fives will cancel. What we're left with is co sign of Fada equals one over the square root of five. So if I want to know, what they did is I'm just trying to take in verse co side of one over square root of five. That's my exact answer for this angle. Plugging that into a calculator to get the angle to the nearest degree. It gives us an angle of approximately 63 degrees. It's a little bit bigger, but it rounds to the nearest degree is 63. So here's my angle between my given vectors

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem