In each case find the eqn of the plane: e) Each point of which is the same distance from the points A(1,-3,7) and B(3,-5,9)

Here's my interpretaion of the question theres 2 points in space A and B and if I were to draw an imaginary line that connects both A and B the plane would then be parallel to that line which makes each point on the plane the same distance from the points A and B.

My attempt:

so I connected A and B to get vector AB=(-5,1,-5)

to get the eqn of the plane I either need to get the normal or have two vectors that lie on the plan that are capableofspanningtheplane

Question

In each case find the eqn of the plane: e) Each point of which is the same distance from the points A(1,-3,7) and B(3,-5,9) 

Here's my interpretaion of the question theres 2 points in space A and B and if I were to draw an imaginary line that connects both A and B the plane would then be parallel to that line which makes each point on the plane the same distance from the points A and B. 

My attempt:

so I connected A and B to get vector AB=(-5,1,-5)

to get the eqn of the plane I either need to get the normal or have two vectors that lie on the plan that are capableofspanningtheplane

anonymous · Answer

Is there a way to get the normal knowing a vector direction that is parallel to the plane?