Let us find the angle between vectors using both and dot product and cross product and let us see what is ambiguity that a cross product can cause.Īngle Between Two Vectors in 2D Using Dot Product Let us consider two vectors in 2D say a = and b =. Let us also see the ambiguity of using the cross-product formula to find the angle between two vectors. Let us see some examples of finding the angle between two vectors using dot product in both 2D and 3D. This is is the formula for the angle between two vectors in terms of the cross product (vector product). Angle Between Two Vectors Using Cross Productīy the definition of cross product, a × b = | a| | b| sin θ \(\hat\) is a unit vector and hence its magnitude is 1. This is is the formula for the angle between two vectors in terms of the dot product (scalar product). Note that the cross product formula involves the magnitude in the numerator as well whereas the dot product formula doesn't.Īngle Between Two Vectors Using Dot Product b is the dot product and a × b is the cross product of a and b.Angle between two vectors using cross product is, θ = sin -1.Angle between two vectors using dot product is, θ = cos -1 [ ( a.Then here are the formulas to find the angle between them using both dot product and cross product: Let a and b be two vectors and θ be the angle between them. But the most commonly used formula of finding the angle between two vectors involves the dot product (let us see what is the problem with the cross product in the next section).
There are two formulas to find the angle between two vectors: one in terms of dot product and the other in terms of the cross product.
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