Question

At what angle θ do the magnitude of A x B equal to A ● B

Answer 1

Step-by-step explanation:

The magnitude of the cross product of two vectors A and B is given by |A x B| = |A| |B| sin(θ), where θ is the angle between the two vectors.

The dot product of two vectors A and B is given by A ● B = |A| |B| cos(θ), where θ is again the angle between the two vectors.

To find the angle θ at which the magnitudes of A x B and A ● B are equal, we set the two expressions equal to each other and solve for θ:

|A x B| = A ● B

|A| |B| sin(θ) = |A| |B| cos(θ)

tan(θ) = 1

θ = 45 degrees

Therefore, at an angle of 45 degrees, the magnitude of A x B is equal to A ● B.