finding volume of the cone by using the dot product

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Vector u = i +j -2 k and v = 2 i + 3 j can be used to form a cone. The cone forms by rotating u about v through 360 degrees.

Find the volume of the cone.

I drew the diagram already, I need the r and h. But I don't know how to solve this question. This question is something to do with vectors.

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Hint: volume of cone = surface of bottom * height/3

assuming $\theta$ is the angle between $u$ and $v$

$$r_{bottom} = \cos{ \theta}*|u|$$

$$h = \sin{ \theta}*|u| = |v|$$