Three Dimension...

The vector equation of line passing through two points $$A(x_1,y_1,z_1),B(x_2,y_2,z_2) $$ is

A line passes through the points (6, -7, -1) and (2, -3, 1). What are the direction ratios of the line ? 

Find vector equation for the line passing through the points $$3\overline i+4\overline j-7\overline k,\overline i-\overline j+6\overline k$$.

The projections of a directed line segment on the coordinate axes are $$12, 4, 3$$ respectively.

From the point $$P(3, -1, 11)$$, a perpendicular is drawn on the line $$L$$ given by the equation $$\dfrac {x}{2} = \dfrac {y - 2}{3} = \dfrac {z - 3}{4}$$. Let $$Q$$ be the foot of the perpendicular.

Find the vector equation of line joining the points $$ (2,1,3)$$ and $$(-4,3,-1)$$

If a line makes the angles $$ \alpha , \beta$$ and $$\gamma$$ with the axes, then what is the value of $$1+\cos 2\alpha +\cos 2\beta+\cos 2\gamma$$ equal to ?

Which of the following represents direction cosines of the line:

The length of perpendicular from the origin to the plane which makes intercepts $$\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5}$$ respectively on the coordinate axes is 

If the normal of the plane makes an angles $$\dfrac {\pi}{4}, \dfrac {\pi}{4}$$ and $$\dfrac {\pi}{2}$$ with positive X-axis, Y-axis and Z-axis respectively and the length of the perpendicular line segment from origin to the plane is $$\sqrt {2}$$, then the equation of the plane is ________.