Three Dimension...

The direction ratios of a line perpendicular to both the lines whose direction ratios are $$3,-2,4$$ and $$1,3,-2$$

The direction cosines of the line $$x=44z+3; y=2-2\sqrt{19}z$$ is...

The distance of the point $$3\hat {i}+5\hat {k}$$ from the line parallel to $$6\hat {i}+\hat {j}  2\hat {k}$$ and passing through the point $$8\hat {i}+3\hat {j}+\hat {k}$$ is 

Three points whose position vectors are $$x\bar{i}+y\bar{j}+z\bar{k}$$, $$\bar{i}+2\bar{j}$$ and $$-\bar{i}-\bar{j}$$ are collinear, then relation between $$x, y, z$$ is?

A line makes equal angles with the coordinate axis. The direction cosines of this line are

A line passes through the point $$(6, -7, -1)$$ and $$(2, -3, 1)$$. Then the sum of the direction cosines of the line, if the line makes acute angle with positive direction of x-axis, is?

The direction Ratio's of normal of the plane through $$(1, 0, 0), (0, 1, 0)$$  which makes angle $$\pi/4$$ with plane $$x+y =3$$ are

If a line makes angles $$\alpha, \beta, \gamma$$ with positive axes, then the range of $$\sin{\alpha}\sin{\beta}+\sin{\beta} \sin{\gamma} +\sin{\gamma} \sin {\alpha}$$ is

The direction ratios of the normal to the plane through $$(1,0,0)$$ and $$(0,1,0)$$ which makes an angle of $$\dfrac{\pi }{4}$$ with the plane $$x + y = 3$$ are-

If $${l}_{1},{m}_{1},{n}_{1}$$ and $${l}_{2},{m}_{2},{n}_{2}$$ are the d.c.s of the two lines, then $${({l}_{1}{l}_{2}+{m}_{1}{m}_{2}+{n}_{1}{n}_{2})}^{2}+{({l}_{1}{m}_{2}-{l}_{2}{m}_{1})}^{2}+{({m}_{1}{n}_{2}-{m}_{2}{n}_{1})}^{2}+{({n}_{1}{l}_{2}-{n}_{2}{l}_{1})}^{2}=$$