Three Dimension...

The direction cosines of a vector $$\displaystyle \hat {i} + \hat {j} + \sqrt {2} \hat {k} $$ are 

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

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

If the line $$\vec{OR}$$ makes angles $$\theta_1, \theta_2, \theta_3$$ with the planes $$XOY, YOZ, ZOX$$ respectively, then $$\cos^2\theta_1+\cos^2\theta_2+\cos^2\theta_3$$ is equal to

The direction cosines of the line segment joining points $$(-3, 1, 2)$$ and $$(1, 4, -10)$$ is.

If a line makes angles $$\alpha, \beta, \gamma$$ and $$\delta$$ with the diagonals of a cube, Then, $$\cos^2\alpha +\cos^2\beta +\cos^2\gamma +\cos^2\delta =\dfrac {a}{b}$$, where $$a$$ and $$b$$ are in lowest form, find $$a+b$$

If $$\alpha, \beta$$ and $$\gamma$$ are the angles which a half ray makes with the positive direction of the axes, then $$\sin^2\alpha+\sin^2\beta+\sin^2\gamma$$ is equal to  

If the three points $$A(1,6), B(3,-4)$$ and $$C(x,y)$$ are collinear, then the equation satisfying by $$x$$ and $$y$$ is

The points $$(k -1, \ k +2), (k, \ k +1), (k +1, \ k)$$ are collinear for