The magnitude of dot and cross product of two vectors is 6√3 and 6 respectively. The angle between _____?
Answer: 30°
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°
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