Three Dimension...

If the projections of the line segment $$AB$$ on the coordinate axes are $$2, 3, 6$$, then the sum of the d.cs of the line $$AB$$ is

If $$l,m,n$$ are the d.cs of a line and $$l=\displaystyle \dfrac{1}{3}$$, then the maximum value of $$l\times m\times n $$ is

lf the projections ofthe line segment$${A}{B}$$ on the $$yz$$-plane, $$zx$$-plane, $$xy$$-plane are $$\sqrt{160}, \sqrt{153},5$$ respectively, then the projection of $${A}{B}$$ on the $${z}$$-axis is

A point $$P$$ lies on a line whose ends are $$A(1,2,3)$$ and $$B(2,10,1).$$ If $$z$$ component of $$P$$ is $$7,$$ then the coordinates of $$P$$ are

lf the direction ratios of two lines are given by the equations $$2l+2m-n=0$$ and $$ml+nl+lm=0$$, then the angle between the two lines is

If OA is equally inclined to OX, OY and OZ and if A is $$\sqrt{3} $$ units from the origin, then A is

If the d.rs of two lines are given by the equations $$l+m+n=0$$ and $$2lm-mn+2nl=0$$, then the angle between the two lines is

lf the $$\mathrm{D.R}$$s of two lines are given by the equations $$l+m+n=0$$ and $$l^{2}+m^{2}-n^{2}=0$$, then the angle between the two lines is:

I. If the d.cs of two non-parallel lines satisfy $$1+m+n=0$$ and $$l^{2}+m^{2}-n^{2}={0}$$, then the angle between the line is $$ \dfrac{\pi }{3}$$ 
II. If the d.rs of two non-parallel lines are $$(0,\lambda, -\lambda)$$ and $$(\mu, 0,-\mu)$$, then angle between the lines is $$\displaystyle \dfrac{\pi}{3} (\lambda>0, \mu>0)$$

Assertion $$({A})$$ . The direction ratios of the line joining origin and point $$(x,y, z)$$ must be $$x, y, {z}$$

Reason (R): lf $$P(x, y, z)$$ is a point in space and $$|{OP}|={r},$$ then the direction cosines of $${O}{P}$$ are $$\displaystyle \dfrac{x}{r}$$ , $$\displaystyle \dfrac{y}{r}$$ , $$\displaystyle \dfrac{z}{r}$$