-plane. The straight line passes through the points ( , , ) and ( , , ) , and therefore, direction ratios of the straight line joining these two points are , , . That is , , So, the straight line is parallel to . Therefore, Required vector equation of the straight line in parametric form is ( ) ( or ( ) ( s where , s t ∈ .
Required cartesian equations of the straight line are or An arbitrary point on the straight line is of the form ( , , ) or ( , , ) s s s Since the straight line crosses the xy -plane, the z -coordinate of the point of intersection is zero. Therefore, we have t − , that is, t = , and hence the straight line crosses the xy -plane at ( , , ) Example . Find the angle made by the straight line x −= − with coordinate axes. If ˆ b is a unit vector parallel to the given line, then ( | .
Therefore, from the definition of direction cosines of ˆ b , we have Vector - - Applications of Vector Algebra cos α = , cos , cos β γ where α β γ are the angles made by ˆ b with the positive x -axis, positive y -axis, and positive z -axis, respectively. As the angle between the given straight line with the coordinate axes are same as the angles made by ˆ b with the coordinate axes, we have α β γ respectively.