Angle Between Vectors

If $\vec A+\vec B+\vec C=\vec0$, $|\vec A|=3$, $|\vec B|=5$, $|\vec C|=7$, then the angle between $\vec A$ and $\vec B$ is

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar unit vectors and $\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{\vec{b} + \vec{c}}{\sqrt{2}}$, then the angle between $\vec{a}$ and $\vec{b}$ is:

If $ |\vec{a}\times \vec{b}| = |\vec{a}\cdot \vec{b}| $, then angle $\theta$ between $\vec{a},\vec{b}$ is:

$ \vec{a} = x\hat{i} - 3\hat{j} - \hat{k},\quad \vec{b} = 2x\hat{i} + x\hat{j} - \hat{k} $ Angle between $ \vec{a} $ and $ \vec{b} $ is acute and angle between $ \vec{b} $ and $ +y $ axis lies in $ \left(\dfrac{\pi}{2}, \pi\right) $ Find $x$.

If a vector $\vec{a}$ makes an equal angle with the coordinate axes and has magnitude 3, then the angle between $\vec{a}$ and each of the three coordinate axes is

If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )