Three Dimension...

ABC is a triangle where $$A = ( 2,3,5 ) , B = ( - 1,2,2 )$$ and $$C (\lambda,5 , \mu )$$ if the median through A is equally inclined to the positive axis then $$\lambda + \mu$$ is 

A line makes angles $$\alpha, \beta, \gamma$$ with the positive direction of the axes of reference. The value of $$\cos{2\alpha}+\cos{2\beta}+\cos{2\gamma}$$ is

Projection of a vector on $$3$$ coordinate axes are $$6, - 3, 2$$ respectively. Then DC's of vector are-

If the foot of the perpendicular from $$(0,0,0)$$ to a plane is $$P(1,2,2)$$. Then, the equation of the plane is

If the points $$\bar a + \bar b,\bar a - \bar b,\bar a + k\bar b$$ are collinear, then  

If the points $$(\alpha, - 1), (2, 1)$$ and $$(4, 5)$$ are collinear, then find $$\alpha $$ by vector method.

$$A(2,3,7),B(-1,3,2)$$ and $$C(q,5,r)$$ are the vertices of $$\Delta ABC$$. If the median through A is equally inclined to the coordinate axes then the coordinates of the vertex C is

A line $$AB$$ in three-dimensional space males angles $${45}^{o}$$ and $${120}^{o}$$ with the positive x-axis and the positive y-axis respectively. If $$AB$$ makes an acute angle $$\theta$$ with the positive z-axis, then $$\theta$$ equal

The Cartesian equation of line $$6x - 2 = 3y + 1 = 2z - 2$$ is given by