A particle is doing simple harmonic motion of amplitude $$0.06 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The maximum velocity of the particle is _________ $$\mathrm{cm} / \mathrm{s}$$.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$P$$ is $$\frac{x \sigma}{\epsilon_0}$$. The value of $$x$$ is _________ (all quantities are measured in SI units).

Radius of a certain orbit of hydrogen atom is 8.48 $$\mathop A\limits^o$$. If energy of electron in this orbit is $$E / x$$. then $$x=$$ ________ (Given $$\mathrm{a}_0=0.529$$ $$\mathop A\limits^o$$, $$E=$$ energy of electron in ground state).

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