# Homework Help: Multiplication using dot product.

1. Oct 9, 2012

### AryRezvani

1. The problem statement, all variables and given/known data

2. Relevant equations

Tan θ=A.B/|A|*|B|

3. The attempt at a solution

A=4i-9j
B=9i-6j

A.B=-18
Magnitude of A = √97
Magnitude of B = √117

Solve that out using Cos-1 (-18/Sqr97*Sqr117) and I keep getting the wrong answer.

2. Oct 9, 2012

### Staff: Mentor

Check the value you've calculated for A.B

3. Oct 9, 2012

### AryRezvani

Ahh just caught that. Replugged in the values, and still came out wrong.

Work:

Plugged in 90/(Sqr97*Sqr117) = .8448190756

Tan-1 (.84481....) = 40.191 degrees.

Plugged that into online homework and it was wrong apparently.

4. Oct 9, 2012

### Staff: Mentor

Check you definition of A.B in terms of magnitudes and angle. You used a correct method in the final line of your first post.

5. Oct 9, 2012

### AryRezvani

Could you specify? Are you referring to A.B=|A||B|Cosθ?

Edit: nevermind, got it!

6. Oct 9, 2012

### Staff: Mentor

Yup. The formula involves a cosine, so why are you employing $tan^{-1}$?

7. Oct 9, 2012

### AryRezvani

Hahaha thanks, took me a while to catch that.. sadly.

8. Oct 9, 2012