The magnitude of dot and cross product of two vectors is 6√3 and 6 respectively. The angle between _____?

The magnitude of dot and cross product of two vectors is 6√3 and 6 respectively. The angle between _____?

Explanation

Given:

|a · b| = 6√3

|a × b| = 6

The dot product is given by:

a · b = |a| |b| cos(θ)

The cross product is given by:

|a × b| = |a| |b| sin(θ)

The ratio of the magnitudes of the cross and dot products is:

|a × b| / |a · b| = tan(θ)

6 / 6√3 = 1/√3 = tan(θ)

θ = arctan(1/√3) = 30°