Three-dimension...

If  l₁ , m₁ , n₁  and  l₂ , m₂ , n₂  are the direction cosines of two lines; and  θ is the acute angle between the two lines; then

Find the equation of the line in cartesian form that passes through the point with position vector    and is in the direction

Equation of a plane passing through three non collinear points (x₁ , y₁ , z₁ ),(x₂ , y₂ , z₂ ) and (x₃ , y₃ , z₃ ) is

Find the Cartesian equation of the plane  

Find the distance of the point (0, 0, 0) from the plane 3x –4y + 12 z = 3

If  a₁ , b₁ , c₁ and  a₂ , b₂ , c₂ are the direction ratios of two lines and  θ is the acute angle between the two lines; then

Find the equation of the line in cartesian form that passes through the point  (–2, 4, –5) and parallel to the line given by  

Vector equation of a plane that contains three non collinear points having position vectors  

The vector and cartesian equations of the planes that passes through the point  (1, 0, –2) and the normal to the plane is

Find the distance of the point (3, –2, 1) from the plane 2x –y + 2z + 3 = 0

Vector equation of a line that passes through the given point whose position vector is   and parallel to a given vector  is

Find the values of p so that the lines   are at right angles.

Vector equation of a plane that passes through the intersection of planes  expressed in terms of a non –zero constant  λ is

Find the equations of the planes that passes through three points (1, 1, 0), (1, 2, 1), (–2, 2, –1)

Find the distance of the point (2, 3, –5) from the plane x + 2y –2z = 9