Question

Try to visualize the set of all points 1x, y, z2 in a coordinate space that are equidistant from the points P10, 0, 02 and Q10, 3, 02. Use the Distance Formula to find an equation for this surface, and observe that it is a plane.

Answer 1

Y plane at y=3/2 contains all the points which will be equidistant from both points P and Q.

Explanation:

As the complete question is not readable, the question is found online and is attached herewith.

By the distance formula, as the point R with coordinates x,y,z is equidistant from P and Q thus

`|PR|=|QR|\\√((x-0)^2+(y-0)^2+(z-0)^2)=√((x-0)^2+(y-3)^2+(z-0)^2)\\(x-0)^2+(y-0)^2+(z-0)^2=(x-0)^2+(y-3)^2+(z-0)^2\\x^2+y^2+z^2=x^2+(y-3)^2+z^2\\y^2=(y-3)^2\\y^2=y^2+9-6y\\-6y=-9\\y=3/2`

So the y plane at y=3/2 contains all the points which will be equidistant from both points P and Q.