Question

At what angle the magnitude of dot product of two Vectors is equal to cross product of two vectors. *​

Answer 1

Answer:

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Answer 2

Explanation:

Let x and y be our two vectors whose dot product and cross product have the same magnitude. So we see know that ∥x×y∥=∥x⋅y∥ so ∥x×y∥∥x⋅y∥=1 . From vector analysis, we know that the dot product of two vectors can be written in terms of their intersecting angle θ as x⋅y=∥x∥∥y∥cosθ and the cross product can be written as ∥x×y∥=∥x∥∥y∥sinθ . We can divide the equations and see 1=∥x×y∥∥x⋅y∥=∥x∥∥y∥sinθ∥x∥∥y∥cosθ=tanθ. From here we can clearly see that tanθ=1 which implies when we restrict our answer to [0,π] thus θ=π4.