Question

If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, what is the angle between the two vectors?

Answer 1

26.57 degrees

Step-by-step explanation:

Let the two vectors be a and b

The dot product of two vectors is expressed as;

a.b = |a||b|cosθ

The cross product is expressed as;

a×b = |a||b|sinθ

If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, then;

|a×b| = 1/2|a.b|

|a||b|sinθ = 1/2|a||b|cosθ

sinθ = 1/2cosθ

2sinθ = cosθ

sinθ/cosθ = 1/2

tanθ = 1/2

θ = arctan(1/2)

θ = 26.57 degrees

Hence the angle between the two vectors is 26.57 degrees