Three Dimension...

If points (1,2), (3 , 5) and (0 , b ) are collinear the value of b is  

The direction angles of the line $$x = 4z + 3, y = 2 - 3z$$ are $$\alpha, \beta$$ and $$\gamma$$, then $$\cos \alpha + \cos \beta + \cos \gamma =$$ ________.

The angle between the lines whose direction cosines are $$\left( \dfrac {\sqrt{3}}{4}, \dfrac {1}{4}, \dfrac {\sqrt{3}}{2} \right)$$ and $$\left( \dfrac {\sqrt{3}}{4}, \dfrac {1}{4}, -\dfrac {\sqrt{3}}{2} \right)$$ is :

Direction cosines of the line $$\cfrac { x+2 }{ 2 } =\cfrac { 2y-5 }{ 3 } ,z=-1$$ are ____

The following lines are $$\hat { r } =\left( \hat { i } +\hat { j }  \right) +\lambda \left( \hat { i } +2\hat { j } -\hat { k }  \right) +\mu \left( -\hat { i } +\hat { j } -\hat { 2k }  \right) $$

$$L$$ and $$M$$ are two points with position vectors $$2\overline { a } -\overline { b } $$ and $$a+2\overline { b } $$ respectively. The position vector of the point $$N$$ which divides the line segment $$LM$$ in the ratio $$2:1$$ externally is

Direction cosines of ray from $$P(1, -2, 4)$$ to $$Q(-1, 1, -2)$$ are

The direction ratios of the line joining the points $$A(4,-3,7)$$ and $$B(1,3,5)$$ are:

If the lines $$x=1+a,y=-3-\lambda a,z=1+\lambda a$$ and $$x=\cfrac { b }{ 2 } ,y=1+b,z=2-b$$ are coplanar, then $$\lambda$$ is equal to

The projection of the join of the two points $$(1,4,5), (6,7,2)$$ on the line whose d.s's are $$(4,5,6)$$ is