1. ## Algebraic Vectors 2

Find the point on the z-axis that is equidistant from the point A(1,-1,1) and B(1,0,-1). Then, find the point not on the z-axis that is equidistant from the point A and B.

Let P be the pointon the z-axis
|PA|=|PB|
Find P

let
(3-2z-z^2)^(0.5)=(2+2z+z^2)^(0.5)
solve y
y=0.25

Therefore point on z-axis is (0,0,0.25)

To find a point not on the z-axis, i found midpoint of a and b

Let that midpoint be Q so, (1,-0.5,0) is my answer.

Please check and let me know! thanks.

2. Originally Posted by skeske1234
Find the point on the z-axis that is equidistant from the point A(1,-1,1) and B(1,0,-1). Then, find the point not on the z-axis that is equidistant from the point A and B.
Therefore point on z-axis is (0,0,0.25)
Let that midpoint be Q so, (1,-0.5,0) is my answer.
Please check and let me know! thanks.
Correct.

Note for the first part it is easier to solve: $1+1+(z-1)^2=1+(z+1)^2$.