Given the plane x + 2y + 3z – 5 = 0, find lines to satisfy the following conditions?
Given the plane x + 2y + 3z – 5 = 0, find lines to satisfy the following conditions:
A line which intersects the plane where it meets the x-axis
More Questions From This User See All
Answers & Comments
Verified answer
The plane intersects the x-axis when y = z = 0, which when plugged into
the plane equation yields x = 5. So all we need is a line that passes through
the point (5,0,0) and is not coincident with the given plane.
As a direction vector for the line we may as well choose the vector normal
to the plane, namely <1,2,3>. So the parametric equations for such a line would be
x = 5 + t, y = 2t, z = 3t.