Three Dimension...

If $$P$$ is a point on the line passing through the point $$A$$ with position vector $$2\overline{i}+\overline{j}-3\overline{k}$$ and parallel to $$\overline{i}+2\overline{j}+\overline{k}$$ such that $$AP=2\sqrt{6}$$ then the position vector of $$P$$ is

Cosine of the angle between two diagonals of a cube is equal to

Area of $$\displaystyle \Delta ABC$$ is

A vector is equally inclined to the $$x$$-axis, $$y$$-axis and $$z$$-axis respectively, its direction cosines are

Find vector equation of line passing through  $$(1,4,1),(1,2,2)$$.

What are the DR's of vector parallel to $$\left( 2,-1,1 \right) $$ and $$\left( 3,4,-1 \right) $$?

The direction cosines of the vectors $$2\vec {i} + \vec {j} - 2\vec {k}$$ is equal to

The Cartesian equation of the plane passing through the point $$(3, -2, -1)$$ and parallel to the vectors $$\overline {b} = \overline {i} - 2\overline {j} + 4\overline {k}$$ and $$\overline {c} = 3\overline {i} + 2\overline {j} - 5\overline {k}$$ is

A straight line is equally inclined to all the three coordinate axes. Then an angle made by the line with the y-axis is

If the foot of the perpendicular from $$(0, 0, 0)$$ to a plane is $$(1, 2, 3)$$, then the equation of the plane is