Three Dimension...

If the points $$(p,0)$$, $$(0,q)$$ and $$(1,1)$$ are collinear, then $$\dfrac { 1 }{ p }+\dfrac { 1 }{ q }$$ is equal to:

The direction ratios of two lines are $$1,-2,-2$$ and $$0,2,1$$. The direction cosines of the line perpendicular to the above lines are 

If the foot of the perpendicular from the origin to a plane is $$\left( a,b,c \right) ,$$ the equation of the plane is 

Are the points (1, 1), (2, 3) and (8, 11) collinear ?

The angle between the straight lines whose direction cosines are given by $$2l+2m-n=0,mn+nl+lm=0$$, is

The planes $$3x-y+z+1=0,5x+y+3z=0$$ intersect in the line $$PQ$$. The equation of the plane through the point $$(2,1,4)$$ and perpendicular to $$PQ$$ is

Equation of the line $$L$$ is -

If direction ratios of the normal of the plane which contains the lines $$\displaystyle\frac{x-2}{3}=\displaystyle\frac{y-4}{2}=\displaystyle\frac{z-1}{1}\;\&\;\displaystyle\frac{x-6}{3}=\displaystyle\frac{y+2}{2}=\displaystyle\frac{z-2}{1}$$ are $$(a,\,1,\,-26)$$, then $$a$$ is equal to

The equation of the plane which contains the lines $$\vec{r}\, =\, \hat{i}\, +\, 2 \hat{j}\, -\, \hat{k}\, +\, \lambda\, (\hat{i}\, +\, 2\, \hat{j}\, -\, \hat{k})$$ and $$\vec{r}\, =\, \hat{i}\, +\, 2 \hat{j}\, -\, \hat{k}\, +\, \mu\, (\hat{i}\, +\, \hat{j}\, +\, 3 \hat{k})$$ must be

The direction ratios of a line followed by the insect during its journey from A to G along the shortest path are