If $a=(1,2,3), b=(2,-1,1), c=(3,2,1)$ and $a \times(b \times c)=\alpha a+\beta b+\gamma c$,then

Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k}$,$\vec{a} \cdot \vec{b}=1$ and $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$. Then $\vec{a}-6 \vec{b}$ is equal to

Which of the following is a true statement?

If $\vec{x} \cdot \vec{y} = 0$ then,$(\vec{y} \times \vec{x}) \times \vec{x} = $ . . . . . . . where,$|\vec{x}| = 1$.

Let $\vec{v}$ be a unit vector which follows the equation $\vec{v} \times \vec{b} = \vec{c}$. Also,$|\vec{b}| = 2$ and $|\vec{c}| = \sqrt{3}$. Then,which of the following is true?

If $\overline{a}, \overline{b}, \overline{c}$ are three vectors with magnitudes $\sqrt{3}, 1, 2$ respectively,such that $\overline{a} \times (\overline{a} \times \overline{c}) + 3 \overline{b} = \overline{0}$,and if $\theta$ is the angle between $\overline{a}$ and $\overline{c}$,then $\sec^2 \theta$ is: