# calc 3

Question
Find an equation of the set of all points equidistant from the points
A(−2, 5, 2) and B(5, 1, −3).

1. 👍 0
2. 👎 0
3. 👁 92
1. Think of two points in space.

The set of all points equidistant from the points is therefore a plane that separates the two points, right in the middle.

Also the line joining the two points would be perpendicular to the plane.

The mid-point between the two points would evidently lie on the plane.

(1) Find the mid-point between the two given points using the mid-point formula. Let this be p0.
(2) Find the vector AB joining the two given points. Then AB is the normal vector to the plane we're looking for.
Let AB=<a,b,c>
(3) Use the components of the normal vector AB (a,b,c) to form the equation of the required plane:
a(x-x0)+b(y-y0)+c(z-z0)=0
where (x0,y0,z0) is the mid-point P0 between A and B.

If you need more details, please post.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Analytic geometry

1. Find the equation of the set of all points P(x,y) that is equidistant from (-3,0) and (3,-5). 2. Find the equation of the set of all points P(x,y) that is twice as far from (-8,8) as from (-2,2). 3. Find the equation of the set

asked by Primma on July 6, 2016
2. ### Math (Analytic Geometry)

1. Find the equation of the set of all points P(x,y) that is equidistant from (-3,0) and (3,-5). 2. Find the equation of the set of all points P(x,y) that is twice as far from (-8,8) as from (-2,2). 3. Find the equation of the set

asked by Justsimplelikeme on July 6, 2016
3. ### Analytic geometry

1. Find the equation of the set of all points P(x,y) that is equidistant from (-3,0) and (3,-5). 2. Find the equation of the set of all points P(x,y) that is twice as far from (-8,8) as from (-2,2). 3. Find the equation of the set

asked by Immaculate on July 6, 2016
4. ### Calculus II

Find an equation of the set of all points equidistant from the points A(−2, 6, 3) and B(5, 3, −3)

asked by julide on January 30, 2014
5. ### Calc

"Find an equation for the set of points P(x, y, z) that are equidistant from the points A(1, 2, 3) and B(4, 0, 1)." Can some one help?

asked by Cody on June 3, 2009
6. ### maths pleaaaase

The point X and Y are 8cm apart Draw a scale drawing of the diagram and draw the locus of points that are equidistant from both points X and Y what do they mean by equidistant Equidistant means the same distance. I'm not a

asked by Mrs. Cunniffe on May 2, 2007
7. ### Geo (locus)

I don't fully get this stuff but some of these I guessed on and some I think I;m close so will someone check/ help me please? * is the answer I put 1. Point A is 0.5 cm from j. k and k are parallel and 1 cm apart. Find the locus

asked by matt on June 12, 2010
8. ### Math

Someone please explain these! The angle between two planes is defined as the angle between their normals. Determine the angle theta between 0 and 90 degrees between the given planes. a) 2x+3y-z+9 = 0 and x+2y+4 = 0

asked by Alex on April 17, 2008
9. ### Math

Someone please explain these! The angle between two planes is defined as the angle between their normals. Determine the angle theta between 0 and 90 degrees between the given planes. a) 2x+3y-z+9 = 0 and x+2y+4 = 0

asked by Alex on April 17, 2008
10. ### Math

Someone please explain these! The angle between two planes is defined as the angle between their normals. Determine the angle theta between 0 and 90 degrees between the given planes. a) 2x+3y-z+9 = 0 and x+2y+4 = 0

asked by Alex on April 17, 2008

More Similar Questions