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?

Answer 4

what is it asking you to do?

Answer 5

oh this stuff here?

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 6

yeah that lol

I figure since it wants ALL points, it needs a time parameter..

Answer 7

but I could be overthinking it >.<

Answer 8

in 3space, the set of all points equidistant from two points P1, P2 is going to be the plane that has the normal which points in the direction of either P1 or P2

so imagine we have these two points P1 and P2

Answer 9

The midpoint of P1P2 is M