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

is given by:

And l = 3 , m = 5 and n = 6 .

Therefore ,

.

The coordinates of the origin are ( 0 , 0 ,0 ) , therefore , , and l = 5 , m = - 2 and n = 3 ,

therefore the equation in Cartesian form is given by:

i.e. .

Here , and

Therefore , the vector equation is :

i.e..

Find the values of p so that the linesare at right angles.

On comparing the given equations with:

, we get:

The given equations can be reduced as:

In the vector form, equation of a plane which is at a distance d from the origin, and is the unit vector normal to the plane through the origin is given by :

In Cartesian co – ordinate system Equation of a plane which is at a distance d from the origin and the direction cosines of the normal to the plane are l, m, n is given by : lx + my + nz = d.