determin arrangement of points in R3

**Craka** · June 5th 2008, 11:40 PM

Given the points A(5,1,3), B(7,9,-1) , C(1, -15, 11) how do I determine if they are or not on a straight line?

**Isomorphism** · June 5th 2008, 11:46 PM

Originally Posted by Craka

Given the points A(5,1,3), B(7,9,-1) , C(1, -15, 11) how do I determine if they are or not on a straight line?

I know a couple of ways to show they are on the same line...

1) Show the area of triangle formed by these points is 0.
2) Form an equation of a line with two points and show the third satisfies it.

**Soroban** · June 6th 2008, 10:53 AM

Hello, Craka!

Another method . . .

Given the points: . $A(5,1,3),\;B(7,9,\text{-}1),\;C(1, \text{-}15, 11)$
how do I determine if they are or not on a straight line?

Find vector $\overrightarrow{AB}\!:\;\;\overrightarrow{AB} \:=\:\langle 7-5,\:9-1,\:\text{-}1-3\rangle \:=\:\langle 2,\:8,\:\text{-}4\rangle \;=\;2\langle 1,\:4,\:\text{-}2\rangle$

Find vector $\overrightarrow{BC}\!:\;\;\overrightarrow{BC} \:=\:\langle 1-7,\:\text{-}15-9,\:11-(\text{-}1)\rangle \:=\:\langle \text{-}6,\:\text{-}24,\:12\rangle \:=\: -6\langle1,\:4,\:\text{-}2\rangle <br />$

Since $\overrightarrow{AB} \parallel \overrightarrow{BC},\;\;A,B,C \text{ are collinear.}$

Thread: determin arrangement of points in R3

LinkBack

Thread Tools

Display

determin arrangement of points in R3

Similar Math Help Forum Discussions

how to determin number of combinations

help me on the arrangement please

any more possible arrangement of AC>AB and BD<BC

determin the symmetry group

Determin an equation from a rational fucntion graph

Search Tags