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3D Geometry: Midpoint, Distance Formulas, and Sphere Equations, Study notes of Calculus

Jaypee University of Engineering & TechnologyCalculus

Formulas for finding the midpoint and distance between two points in three-dimensional space. It also includes equations for finding the center and radius of a sphere. Several examples of calculating the distance between given points and finding the sphere's center and radius using the provided equations.

Typology: Study notes

2012/2013

Uploaded on 02/11/2013

amit-kumar
amit-kumar 🇮🇳

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Obj ective 10
Midpoint and Distance Formulas in 3D
Find the distance between points
PI
and
P2.
jPt
I
d~o\u+
1)
PI(-5,
6,8)
and
P2(-3, 7,10)
2)
PI
(-8,3,2)
and
P2(-2,
1,5)
4)
PI
(4,
-3,
-8)
and
P2(5,
-4,
-9)
Find the center and radius
of
the sphere.
5)
x2 + (y + 7)2 + (z -1)2 = 16
7)
x2 +
y2
+
z2
-lOx -
Sy
+ 20z = -116
8)
x2 +
y2
+
-I2x
4y-16z
-79
pf3
pf4

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Obj ective 10

Midpoint and Distance Formulas in 3D

Find the distance between points 1) PI(-5, 6,8) and P2(-3, 7,10) PI and P2. jPtI d~o\u+

  1. PI (-8,3,2) and P2(-2, 1,5)

  2. PI (4, -3, -8) and P2(5, -4, -9)

Find the center and radius5) x 2 + (y + 7)2 + (z - 1)2 of the sphere. = 16

  1. x^2 + y2 + z2 - lOx - Sy + 20z = -
  2. x^2 + y2 + -I2x 4y-16z -

1)\s+OUC.~ \V\ ~ 'D (Eve. kdt'al/\ )

'PI ('t I, 'I t > Xi))? L (X 'l) Y<- J '22.)

M i o~ PO"'-t

')( '1 t '2 I

S'PIt£RE (I<M~D)

C~(l C (o.. I b, 0 ) 'i<pro'u s. 'R ( )( - (A) 2.^ -t ('i -- b) '2..^ --+ ('2 - cJ 'L^ :::. 'k'< *L. ----.*

rt. '< ( X-f~) -f (Y -* '6 ) ~ ~ C (-4 )- 8) - ¥) ~