If $a = 3i - j + 2k,$ $b = 2i + j - k$ and $c = i - 2j + 2k,$ then $(a \times b) \times c$ is equal to

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

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b} \cdot \vec{c} = 0$ and $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\vec{b} - \vec{c}}{2}$. If $\vec{d}$ is a vector such that $\vec{b} \cdot \vec{d} = \vec{a} \cdot \vec{b}$,then $(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d})$ is equal to

Which of the following statements is true regarding the vector triple product $(a \times b) \times c$?

If $(\vec{a} \times \vec{b}) \times \vec{c} = \vec{a} \times (\vec{b} \times \vec{c})$ where $\vec{a}, \vec{b},$ and $\vec{c}$ are any three vectors such that $\vec{a} \cdot \vec{b} \neq 0$ and $\vec{b} \cdot \vec{c} \neq 0$,then $\vec{a}$ and $\vec{c}$ are:

If $a \cdot b = \beta$ and $a \times b = c$, then $a =$