Equation of the plane passing through the point (2, 0, 5) and parallel to the vectors $$\widehat i - \widehat j + \widehat k$$ and $$3\widehat i + 2\widehat j - \widehat k$$ is

The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines of $$\overline{\mathrm{OP}}$$ are

The equation of the plane containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ and the point $$(0,7,-7)$$ is

The equation of a line passing through $$(3,-1,2)$$ and perpendicular to the lines $$\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(2 \hat{i}-2 \hat{j}+\hat{k})$$ and $$\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\mu(\hat{i}-2 \hat{j}+2 \hat{k})$$ is