Cross product and Dot product problem

[PsychonautQQ]

Homework Statement

if v x w = <5,5,-2>
(v cross w)

and

v * w = 6
(v dot w)

then what is the tan(θ) between the two vectors v and w?

The Attempt at a Solution

well I was thinking v x w = |v||w|sinθ
as well as v dot w (v*w) = |v|w|cosθ

divide one equation by the other and the absolute values on the right cancel out,
but then you get a vector divided by a number on the left side equals tanθ

is this how you do this problem?

 

[Jolb]

You have a problem with the first equation in your attempt at solution. It should read:
|v × w| = |v| |w| sinθ

You are right that v × w is a vector, and the correct equation for it would be:
v × w = |v| |w| sinθ n
where n is the unit vector perpendicular to both v and w given by the right-hand rule.

 

[Mark44]

To expand on what Jolb said, since you're given that v x w = <5, 5, -2>, you have enough information to find |v x w|.