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Question

Suppose 𝑣⃗⋅𝑤⃗=4v→⋅w→=4 and ||𝑣⃗×𝑤⃗||=2||v→×w→||=2, and the angle between 𝑣⃗v→ and 𝑤⃗w→ is 𝜃θ. Find

tan𝜃=?

𝜃=?

Answer 1

If we know that the dot product is 4, and the cross product has magnitude 2, we can utilize the following identities:

Therefore, if we divide the magnitude of the cross product by the dot product, which is 2/4=.5, we get the tangent of theta. To get theta itself, we simply take the inverse tangent of this ratio, which is the inverse tangent of .5, which is about .46 radians