The volume of a tetrahedron with vertices $A(5, -1, 1)$, $B(7, -4, p)$, $C(1, -6, 10)$, and $D(-1, -3, 7)$ is $11 \text{ cubic units}$. Find one of the values of $p$.

Let three vectors $\vec{a}, \vec{b}$ and $\vec{c}$ be such that $\vec{a} \times \vec{b} = \vec{c}$,$\vec{b} \times \vec{c} = \vec{a}$ and $|\vec{a}| = 2$. Then which one of the following is not true?

If the points with position vectors $\hat{i}-2 \hat{j}+3 \hat{k}$, $2 \hat{i}+3 \hat{j}-4 \hat{k}$, $-3 \hat{i}+\hat{j}-5 \hat{k}$, and $a \hat{i}-2 \hat{j}+4 \hat{k}$ are coplanar, then $a=$

Let $p, q, r$ be three non-coplanar vectors and $b = p \times q$. If $a, b, c$ denote the coterminous edges of a parallelepiped, then its height with the base having $a$ and $c$ is

If $x \cdot a = 0, x \cdot b = 0$ and $x \cdot c = 0$ for some non-zero vector $x$,then the true statement is

If the vectors $2i - j + k$,$i + 2j - 3k$,and $3i + \lambda j + 5k$ are coplanar,then $\lambda = $