# Given vectors how to find third equation

1. Jun 2, 2014

### mill

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

If |v|=4, |w|=3 and the angle between and is pi/3, find |2v −w|

2. Relevant equations
$cosθ=\frac {v dot w} {|v||w|}$

3. The attempt at a solution
$6= v dot w$

This is as far as I got. How would I find the separate values of v and w for the equation?

2. Jun 2, 2014

### ehild

Very good! How is the absolute value of a vector defined with dot product by itself?
You do not need to know the individual vectors. You need the absolute value of 2v-w.

ehild

3. Jun 2, 2014

### mill

u dot u = $|u|^2$ so |u|= $\sqrt {u dot u}$ ?

Possibly, that becomes |2v-w|=sqrt(something?) or would |?|(1/2)=|2v-w|

I'm afraid I don't see how things are connecting to the third equation though.

1/2 = (something analogous to u dot v)/|2v-w|?

Last edited: Jun 2, 2014
4. Jun 2, 2014

### Staff: Mentor

Start from that definition. What then is $\sqrt{(2v-w) \cdot (2v-w)}$?

5. Jun 2, 2014

### mill

Got it, thanks.

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