Given vectors how to find third equation

[mill]

Homework Statement

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

Homework Equations

$cosθ=\frac {v dot w} {|v||w|}$

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?

 

[ehild]

Homework Statement

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

Homework Equations

$cosθ=\frac {v dot w} {|v||w|}$

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?

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

 

[mill]

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

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|?

 

[DrClaude]

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

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

 

[mill]

Got it, thanks.