Three Dimension...

The direction ratios of the joining $$A(1,\,2,\ 1)$$ and $$(2,\ 1,\ 2)$$ are

The direction ratios of $$AB$$ are $$- 2, 2, 1$$ . If coordinates of A are $$( 4,1,5 )$$ and $$l( A B ) = 6$$ , then coordinates of $$ B $$ ?

If $$\bar {a}, \bar {b}$$ and $$\bar {c}$$ are non-zero non collinear vectors and $$\theta(\neq 0 , \pi)$$ is the angle between $$\bar {b}$$ and $$\bar {c}$$ if $$(\bar {a}\times \bar {b}) \times \bar {c}=\dfrac {1}{2} |\bar {b}|\bar {c}|\bar {a}$$. then $$\sin \theta =$$

A line d.c's proportional to $$(2,1,2)$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$. Then the coordinates of each of the points of intersection are given by

If $$\frac{x-14}{l}=\frac{y-2}{m}=\frac{z+1}{n}$$ is the equation of the line through (1,2,-1) and (-1,0,1), then (l,m,n) is 

If $$A = (1,2,3) , B  = (2,10,1), Q$$ are collinear points and $$Q_{x}=-1$$ then $$Q_{z}$$ is

The direction cosines of a vector $$ \overrightarrow { A }  $$ are $$ \cos \alpha = \frac {4} { 5 \sqrt {2}} , \cos\beta =\frac { 1 }{ \sqrt { 2 }  } , \cos\gamma =\frac { 3 }{ 5\sqrt { 2 }  }  $$ then, the vector $$ \overrightarrow {A} $$ is 

The direction cosines to two lines at right angles are (1,2,3) and (-2,$$\frac{1}{2}$$,$$\frac{1}{3}$$), then the direction cosine perpendicular to both given lines are:

The vector equation of line passing through the point $$(-1,-1,2)$$ and parallel to the line $$2x-2=3y+1=6z-2$$

The direction ratios of the line joining the points $$(4, 3, -5)$$ and $$(-2, 1, -8)$$ are