What is the angle between resultant of $A+B$ and $\mathbf{A} \times \mathbf{B}$.

The $$x, y$$ components of vector $$\mathbf{P}$$ have magnitudes 1 and 3 and $$x, y$$ components of resultant of $$\mathbf{P}$$ and $$\mathbf{Q}$$ have magnitudes 5 and 6, respectively. What is the magnitude of $$\mathbf{Q}$$ ?

The resultant of two vector $$\mathbf{A}$$ and $$\mathbf{B}$$ is $$\mathbf{C}$$. If the magnitude of $$\mathbf{B}$$ is doubled, the new resultant vector becomes perpendicular to A. Then, the magnitude of $$\mathbf{C}$$ is

Two vectors of same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is