If $$(2,3, c)$$ are the direction ratios of a ray passing through the point $$C(5, q, 1)$$ and also the mid-point of the line segment joining the points $$A(p,-4,2)$$ and $$B(3,2,-4)$$, then $$c \cdot(p+7 q)=$$

If the equation of the plane which is at a distance of $$1 / 3$$ units from the origin and perpendicular to a line whose directional ratios are $$(1,2,2)$$ is $$x+p y+q z+r=0$$, then $$\sqrt{p^2+q^2+r^2}=$$

The point of intersection of the lines $$\mathbf{r}=2 \mathbf{b}+t(6 \mathbf{c}-\mathbf{a})$$ and $$\mathbf{r}=\mathbf{a}+s(\mathbf{b}-3 \mathbf{c})$$ is

If the point $$(a, 8,-2)$$ divides the line segment joining the points $$(1,4,6)$$ and $$(5,2,10)$$ in the ratio $$m: n$$, then $$\frac{2 m}{n}-\frac{a}{3}=$$