List of top Physics Questions on Scalar Triple Product

For three vectors \( \vec{A} = (-xi - 6j - 2k), \) \( \vec{B} = (-i + 4j + 3k) \) and \( \vec{C} = (-8i - j + 3k), \) if \( \vec{A} \cdot (\vec{B} \times \vec{C}) = 0, \) then value of x is ___________.

Let $\hat{a}, \hat{b}, \hat{c}$ be unit vectors such that $\hat{a}\times(\hat{b}\times\hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c})$. The angle between $\hat{a}$ and $\hat{c}$ is:

Let $\vec{\alpha} = \hat{i} + 2\hat{j} - \hat{k}$, $\vec{\beta} = 2\hat{i} - \hat{j} + 3\hat{k}$, and $\vec{\gamma} = 2\hat{i} + \hat{j} + 6\hat{k}$.If $\vec{\alpha}$ and $\vec{\beta}$ are both perpendicular to a vector $\vec{\delta}$ and $\vec{\delta} \cdot \vec{\gamma} = 10$, then the magnitude of $\vec{\delta}$ is: }