Two vectors of the same magnitude have a resultant equal to either of the two vectors. The angle between the two vectors is: (in $^{\circ}$)

If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,find the magnitude and direction of $\overrightarrow A + \overrightarrow B$.

Magnitudes of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in the same direction $(\theta = 0^{\circ})$ and $(ii)$ in the opposite direction $(\theta = 180^{\circ})$,find the magnitude of the resultant vector in each case.

Let $\vec{A}$ and $\vec{B}$ be two non-zero vectors of different magnitudes. Which one of the following is the correct equation?

Give the equations to find the magnitude and direction of the resultant vector of two vectors $\vec{A}$ and $\vec{B}$ that are inclined at an angle $\theta$ to each other.

Given $\vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k})$,$\vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k})$. The value of $(\vec{A}+\vec{B}) \cdot \vec{C}$ will be