Straight lines in Space

To determine a straight line we need a point and a vector, which is called direction vector:

In coordinates

If we work out λ and equalize them:

By doing the cross-product and simplifying in two of them, we obtain:

Example 1:

Example 2:

Exercises:

1.- Find the equations of the straight line that passes through the origin and has the direction of r:

2.- Find the parametric equations of the straight line s:

Solutions:

1.-

2.-