Three Dimension...

Vector equation of the line $$6x - 2 = 3y + 1 = 2z - 2$$ is 

The equation of the plane passing through $$(2, -3, 1)$$ and is normal to the line joining the points $$(3, 4, -1)$$ and $$(2, -1, 5)$$ is given by

The points with position vectors $$60\hat{i}+3\hat{j}$$, $$40\hat{i}-8\hat{j}$$, $$a\hat{i}-52\hat{j}$$  are collinear if

Direction cosines $$l, m, n$$ of two lines are connected by the equation $$l-5m+3n=0$$ and $$7l^{2}+5m^{2}-3n^{2}=0$$. The direction cosines of one of the lines are

Can $$\dfrac{1}{\sqrt{3}}, \dfrac{2}{\sqrt{3}}, \dfrac{-2}{\sqrt{3}}$$ be the direction cosines of any directed line?

If the $$d.c's$$ of two lines are connected by the equations $$l + m + n = 0, l^2 + m^2 - n^2 = 0$$, then angle between the lines is

The direction cosines of a line which is equally inclined to axes, is given by

The equation of the plane containing the line 
$$\vec r = \hat i + \hat j + t\left( {2\hat i + \hat j + 4\hat k} \right)$$, is

A line passes through the points $$(6, -7, -1)$$ and $$(2, -3, 1)$$. The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, is?

If $$P$$ be the point $$(2,6,3)$$ then the equation of the plane trough $$P$$, at right angles to $$OP$$, where  $$'O'$$ is the origin is