Three Dimension...

The angle between the lines $$\cfrac{x-2}{2}=\cfrac{y-1}{7}=\cfrac{z+3}{-3}$$ and $$\cfrac{x+2}{-1}=\cfrac{y-4}{2}=\cfrac{x-5}{4}$$ is

The Cartesian equation of a line are $$\cfrac{x-2}{2}=\cfrac{y+1}{3}=\cfrac{z-3}{-2}$$. What is its vector equation?

If the points $$A(-1,3,2),B(-4,2,-2)$$ and $$C(5,5,\lambda)$$ are collinear then the value of $$\lambda$$ is

The direction cosines of the perpendicular from the origin to the plane $$\vec{r}\cdot (6\hat{i}-3\hat{j}+2\hat{k})+1=0$$ are?

The direction consines of the line drawn from $$P\left ( -5,3,1 \right )\,to\,Q\left ( 1,5,-2 \right )$$ is

The equation of the plane which passes through the x-axis and perpendicular to the line $$\dfrac {(x - 1)}{cos\theta} = \dfrac {(y + 2)}{sin\theta} = \dfrac {(z - 3)}{0}$$ is

The direction cosines of the normal to the plane $$5y+4=0$$ are?

If O is the origin and $$P(1, 2, -3)$$ is a given point, then the equation of the plane through P and perpendicular to OP is?

 If the directions cosines of a line are $$ k, k, k, $$ then

What is the equation of the plane which passes through the z-axis and is perpendicular to the line  
$$\dfrac{x - a} {\cos \theta} = \dfrac{y +  2} {\sin \theta} = \dfrac{z - 3} {0} ?$$