Three Dimension...

The vector equation $$r=i-2j-k+t(6j-k)$$ represents a straight line passing through the points:

A line makes the same angle $$\theta$$ with each of the $$X$$ and $$Z$$-axes. If the angle $$\beta$$, which it makes with $$Y$$-axis, is such that $$\sin ^{ 2 }{ \beta  } =3\sin ^{ 2 }{ \theta  } $$, then $$\cos ^{ 2 }{ \theta  } $$ equals

Equation to a line parallel to the vector $$2\hat{i}-\hat{j}{+}\hat{k}$$ and passing through the point $$\hat{i}+\hat{j}{+\hat{k}}$$

The points with position vectors $$ 60i + 3j,  40i -8j$$ and $$ ai -52j $$ are collinear if

If the direction cosines of a line are $$\left(\displaystyle \dfrac{1}{c},\dfrac{1}{c},\dfrac{1}{c}\right)$$ then $$c=$$______

$$l = m =n = 1$$ represents the direction cosines of 

The direction ratios of the diagonal of the cube joining the origin to the opposite corner are (when the $$3$$ concurrent edges of the cube are coordinate axes)

If $$P(x, y, z)$$ moves such that $$x=0, z=0$$, then the locus of $$P$$ is the line whose d.cs are

If the points $$A(\overline{a}), B(\overline{b}), C(\overline{c})$$ satisfy the relation $$3\mathrm{a}-8\mathrm{b}+5\mathrm{c}=0$$ then the points are