If we have two vectors, A and B, and we know what vector A is and what the angle between A and B is, is there any way to determine the possibilities of vector B? (Assume the vectors are in two-dimensional space)
[Math] Determining Vector Given One Vector and the Angle Between the Two Vectors
vectors
Best Answer
If we assume a signed angle (e.g., counterclockwise is positive), then yes. If not, then no.
From OP Comment
If we know the length of $\vec{B}$ i.e., $|B|$, and the components of $\vec{A}$, then we can normalize A, left-multiply by the rotation matrix, then re-scale:
$$\vec{B}=\begin{bmatrix}\cos\theta & -\sin\theta &\\\sin\theta & \cos\theta \end{bmatrix}\frac{|B|\vec{A}}{|A|}$$
If you don't know $|B|$, then set it to $1$ in the above formula to get the direction of $B$