Question

P1 = (3,2,-1) and P2 = (7,-5,4) are points

Do I need to parametrize this?

Answer 1

a) Find the midpoint of the line segment joining P1 and P2

b) Find an equation in x, y and z for the set of all point equidistant from P1 and P2

c) What is the graph of the equation you found in b?

Answer 2

So the line segment connecting the 2 is (4 , -7 , 5)

Midpoint being (2 , -7/2 , 5/2)

That's part a)

Answer 3

So part b) I'm not sure if I need to parametrize this? Since it asks for all points I feel like we need the position vector

\[\large R(t) = (3 , 2, -1) + t<4, -7, 5>\]

Is this what I need to do?

Or, would I need to use that midpoint (2, -7/2, 5/2) as the direction vector?