How do I find a third vector in the same plane as the first two vectors but at a angle from one of the vectors

Question

anonymous · Answer

since they are all coplanar vectors, the third vector can be assumed as xi+yj where i and j are unit vectors in the direction of X, Y axes respectively. now you can use the definition of DOT product and solve for x and y.

amistre64 · Answer

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then rotate the vectors as needed to align with the known vectors

X = xcos($\theta$)-ysin($\theta$)
Y = xsin$\theta$)+ycos($\theta$)