Three-dimension...

Let    be the position vector of an arbitrary point P(x, y, z). Cartesian form of the equation of line passes through two points (x₁ , y₁ , z₁ ) and (x₂ , y₂ , z₂ ) is:

Find the vector equation of the line that passes through the origin and (-6,2,1).

The Cartesian equation of the line which passes through the point (2, -2, -1) and parallel to the line   , is given by

If the vector equation of a line is   find its caryesian equation.

The vector form of the equation is. The Cartesian equation of the line is:

Let the coordinates of the given point A be (x₁ , y₁ , z₁ ) and the direction ratios of the line be a, b, c. If the co-ordinates of any point P is (x, y, z), then the equation of the line in Cartesian form is:

Let    be a position vector of A with respect to the origin O and    be a position vector of an arbitrary point. The equation of line which passes through A and parallel to a vector   is:

The Cartesian equation of the line passing through the points (-3, 1, 0) and (1, 2, 3) is:

The Cartesian equation of the line which passes through the origin and parallel to the line   , is given by

Find the Cartesian equation of the line that passes through the point (-3,-4,-2) and (3,4,2).