# Vectors: finding the angle between two vectors using dot product method when you don

1. Mar 1, 2012

### Jane K

1. The problem statement, all variables and given/known data
The vector a=2 and vector b=1. The vectors a+5b and 2a-3b are perpendicular. Determine the angle between a and b .

2. Relevant equations
The dot product a•b=lallblcosθ

3. The attempt at a solution
I've tried a few things but none of it really makes sense. I'm worried that maybe this question doesn't call for the dot product method but I've become fixed on it.

2. Mar 1, 2012

### LCKurtz

Re: Vectors: finding the angle between two vectors using dot product method when you

You don't have a vector a = 2 and b = 1, those are scalars. Perhaps you mean their magnitudes are 2 and 1? What do you get if you dot a+5b and 2a-3b together?

3. Mar 2, 2012

### Jane K

Re: Vectors: finding the angle between two vectors using dot product method when you

"the vectors a and b have lengths 2 and 1, respectively." I'm trying to find the angle between the two. The dot product for the perpendicular vectors a+5b and 2a-3b would be zero... im stuck:P.

4. Mar 2, 2012

### LCKurtz

Re: Vectors: finding the angle between two vectors using dot product method when you

Show us what you get in terms of a and b when you dot those two vectors together and set it equal to 0.

5. Mar 2, 2012

### SammyS

Staff Emeritus
Re: Vectors: finding the angle between two vectors using dot product method when you

"FOIL" works for vectors .

$\left(\vec{a}+\vec{b}\right)\cdot\left(\vec{c}+ \vec{d}\right)=\vec{a}\cdot\vec{c}+\vec{a}\cdot \vec{d}+\vec{b}\cdot\vec{c}+\vec{b}\cdot\vec{d}$​

6. Mar 2, 2012

### Deveno

Re: Vectors: finding the angle between two vectors using dot product method when you

what SammyS means is that the dot product is bilinear, it is linear in each variable:

if a,b,c are vectors, and r is a scalar:

a.(b+c) = a.b + a.c
(a+b).c = a.c + b.c

a.(rb) = r(a.b)
(ra).b = r(a.b)

also, a.b = b.a (the dot product is symmetric).

thus (a+5b).(2a-3b) = 2(a.a) + 5(b.a) - 3(a.b) - 15(b.b)

a.a = |a|2, for any vector a.

you are given |a| and |b|, and you are given that the dot product (a+5b).(2a-3b) = 0.

if you can deduce what a.b is, then you can figure out the angle:

θ = arccos[(a.b)/(|a||b|)]

7. Mar 2, 2012

### Jane K

Re: Vectors: finding the angle between two vectors using dot product method when you

Thank-you everyone!
This really helped:)