Three Dimension...

$$ox, oy$$ are positive $$\mathrm{x}$$-axis, positive $${y}$$-axis respectively where $${O}=(0, 0,0)$$ . The $${d.c.}$$s of the llne which bisects $$\angle xoy$$ are

The direction cosines of the line passing through $$\mathrm{P}(2,3,-1)$$ and the origin are

If $$A$$ is $$(2, 4, 5),$$ and $$B$$ is $$(-7, -2, 8)$$, then which of the following is collinear with$$A$$ and $$B$$ is

lf a line makes $$\dfrac{\pi }{3},\dfrac{\pi }{4}$$ with the $$x$$-axis, $${y}$$-axis respectively, then the angle made by that line with the $$z$$- axis is

If $$l, m, n$$ are the d.cs of the line joining $$(5, -3, 8)$$ and $$(6, -1, 6)$$ then $$l + m + n=$$

If $$\dfrac{1}{2}, \displaystyle \dfrac{1}{2}$$, $$n(n<0)$$ are the dcs of a line, then the angle made by that line with $$OZ$$ where $$O=(0,0,0)$$ is

If the direction ratios of two lines are given by $$3lm-4ln+mn=0$$ and $$l+2m+3n=0$$, then the angle between the lines is

If $$P = (3, 4, 5)$$, $$Q= (4, 6, 3)$$, $$R= (-1, 2, 4)$$ and $$S=(1, 0, 5)$$ are four points, then the projection of $$RS$$ on $$PQ$$ is

If the projections of the line segment $$AB$$ on the coordinate axes are $$2, 3, 6$$, then the square of the sine of the angle made by $$AB$$ with $$x=0$$, is

If $$(2, 1, 3)$$ and $$(-1, 2, 4)$$ are the extremities of a diagonal of a rhombus then the d.rs of the other diagonal are