##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# Vector Operations in 3D - Problem 2

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

Let's find the angle between two vectors; A which has components 3, 0, 4, and B which has components -1, 3, 4. I've drawn the two vectors here, and so what we're looking for is this angle between them. So let's call that angle theta. The cosine theta is A.B divided by the magnitude of A times the magnitude of B.

So we're going to need to calculate the magnitudes. Let's do the magnitude of A first. It's the square root of 3², 9 plus 0², plus 4² is 16. So 9 plus 0, plus 16 that's 25 and the square root of 25 is 5. What about the magnitude of B? It's the square root of 1 plus 9, plus 16. 1 plus 9 plus 16 that's root 26. So let's start filling this in. Cosine of theta equals A.B, what's A.B? 3 times -1, -3, plus 0 times 3, 0, plus 4 times 4, 16, all over 5 times root 26. So that means cosine theta equals 13 over 5 root 26.

Let's use our calculators to calculate theta. Theta is going to be inverse cosine of 13 over 5, root 26. So the inverse cosine 13 divided by 5 root 26, 59.3 degrees. So the angle between these two vectors is 59.3 degrees.

Now remember, you find the angle between vectors the same way in three dimensions as in two dimensions using this formula.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

###### Get Peer Support on User Forum

Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.

##### Concept (1)

##### Sample Problems (2)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete