If the Cartesian equation of a line is $$6 x-2=3 y+1=2 z-2$$, then the vector equation of the line is

The volume of parallelopiped, whose coterminous edges are given by $$\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \vec{v}=\hat{i}+\hat{j}+3 \hat{k}, \bar{w}=2 \hat{i}+\hat{j}+\hat{k}$$ is 1 cu. units. If $$\theta$$ is the angle between $$\bar{u}$$ and $$\bar{w}$$, then the value of $$\cos \theta$$ is

A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum

The ratio of wavelengths for transition of electrons from $$2^{\text {nd }}$$ orbit to $$1^{\text {st }}$$ orbit of Helium $$\left(\mathrm{He}^{++}\right)$$ and Lithium $$\left(\mathrm{Li}^{++1}\right)$$ is (Atomic number of Helium $$=2$$, Atomic number of Lithium $$=3$$ )