To find the angle between two vectors, you need to use this form:
a ∙ b / (|ab|) = cos(θ)
θ = arccos(a ∙ b / (|ab|)) where a and b are vectors.
Compute the dot product and the norm of |a| and |b|. Then, compute the angle between the vectors.
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Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
Multiply the product of their magnitudes by the cosine of the angle between them.
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.