Can you visualize a line perpendicular to a plane?
That line has a direction vector. Any vector in the plane is perpendicular to that direction vector.
This question is in the review for the Dot Product section. Question How many lines pass through the point (4, 5, 6) and are perpendicular to the vector (1, 2, 3) ? The follow-up question says to find the equation for the region that contains all the lines passing through (4, 5, 6) and perpendicular to (1, 2, 3). Answer The answer to the follow-up is in the linear form of the equation of a plane. So, I'm assuming that the answer is an infinite number of lines? But I do not actually understand the concept behind that. Any suggestions on how to approach this problem?