Three Dimension...

The equation of the plane passing through the point $$(1, 1, 1)$$ and perpendicular to the planes $$2x+y-2z=5$$ and $$3x-6y-2z=7$$ is?

The acute angle between two lines such that the direction cosines $$l,\  m,\ n$$ of each of them satisfy the equation $$l+m+n=0$$ and $$l^2+m^2-n^2=0$$ is 

The direction cosines of the ray $$P(1,-2,4)$$ and $$Q(-1,1,-2)$$ are

The measure of the angle between the lines, whose direction numbers are $$l,m,n$$ and $$m-n,n-l,l-m$$ is ______

The acute angle between two lines such that the direction cosines l,m,n of each of them satisfy the equations $$l+m+n=0$$ and $${ l }^{ 2 }+{ m }^{ 2 }-{ n }^{ 2 }=0$$ is :-

Find in a symmetrical form, the equations of the line formed by the planes $$x+y+z+1=0, 4x+y-2z+2=0$$ and find its direction-cosines.

The equation of plane passing through $$(4, 5, -1)$$ having normal $$3\hat{i}-\hat{j}+\hat{k}$$ is ___________.

Vector equation of line $$\dfrac{3-x}{3}=\dfrac{2y-3}{5}=\dfrac{z}{2}$$ is __________ $$k\in R$$.

The vector equation of the plane which is at distance of $$10$$ unit from the origin and perpendicular to the vector $$4i+4j-2k$$ is

A line making angles $$45^o$$ and $$60^o$$ with the positive direction of $$x-$$ axis and $$y-$$ axis respectively. Then the angle made by the line with positive direction of $$z-$$ axis is