Let p, q and r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies equation p x {(x - q) x p} + q x {(x - r) x r} + r x {(x - p) x r} = 0, then x is given by
Let: $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}$ be there vectors If $\vec{r}$ is a vector such that, $\vec{r} \times \vec{b}=\vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a}=0$, then $25|\vec{r}|^2$ is equal to
\(A\) is a neutral organic compound (M.F.: \(C_8H_9ON\)). On treatment with aqueous \(Br_2/HO^-\), \(A\) forms a compound \(B\) which is soluble in dilute acid. \(B\) on treatment with aqueous \(NaNO_2/HCl\) (0--5\(^\circ\)C) produces a compound \(C\) which on treatment with \(CuCN/NaCN\) produces \(D\). Hydrolysis of \(D\) produces \(E\) which is also obtainable from the hydrolysis of \(A\). \(E\) on treatment with acidified \(KMnO_4\) produces \(F\). \(F\) contains two different types of hydrogen atoms. The structure of \(A\) is
