Three Dimension...

If the d.rs of $$OA$$ and $$OB$$ are $$1, -1, -1$$ and $$2, -1, 1$$, then the d.cs of the line perpendicular to both $$OA$$ and $$OB$$ are

$$A = (1, 2, 3), B = (4, 5, 7), C = (-4, 3, -6), D =(2, k, 2)$$ are four points. If the lines $$AB$$ and $$CD$$ are parallel, then $$k =$$

lf $${P}(x,y,z)$$ is a point on the line segment  joining $${A}(2,2,4)$$ and $${B}(3,5,6)$$ such that projection of $$\overline{OP}$$ on axes are $$\displaystyle \dfrac{13}{5},\dfrac{19}{5},\dfrac{26}{5}$$ respectively, then $${P}$$ divide $${A}{B}$$ in the ratio

The projections of a line segment on $$x,y\ and\ z$$ axes are respectively $$\sqrt{2},3,5$$. The length of the line segment is

If the d.rs of two lines are $$1, -2, 3$$ and $$2, 0, 1$$, then the d.rs of the line perpendicular to both the given lines is

lf $${A}=(3,1, -2), {B}=(-1,0,1)$$ and $$l,m$$ are the projections of $${A}{B}$$ on the $${y}$$-axis, $$zx$$-plane respectively, then $$3l^{2}-m+1=$$

The d.rs of the lines $$x=  ay + b$$, $$z= cy + d$$ are:

Find the angles between the lines, whose direction cosines are give by the equation $${ l }^{ 2 }-{ m }^{ 2 }+{ n }^{ 2 }=0,l+m+n=0$$

The projection of the line segment joining $$(0, 0, 0)$$ and $$(5, 2, 4)$$ on the line whose direction ratios are $$2, -3, 6$$ is

lf $$AB \perp BC$$, then the value of $$\lambda$$ equal, where $$ A(2k,2,3), B(k,1,5),C(3+k,2,1)$$