Question

Determine whether the points P1, P2, and P3 lie on the same line.
P1(6, 9, 7), P2(9, 2, 0), P3(0,−5,−3)

Answer 1

@ganeshie8

Answer 2

please help me learn to do this. thanks

Answer 3

@Loser66

Answer 4

do you know how to write the equation of a line given two points?

Answer 5

yes but this is in 3D not 2D

Answer 6

yes, you will have to write a parametric equation

Answer 7

x=x0+at , y=y0+bt , z=z0+ct the form for the equation of the line in 3D

Answer 8

i need to find the vector parallel to the line? i think but how shd i go about doing so

Answer 9

just take the first two points P1 and P2
(P2-P1) is the vector connecting P2 and P1

Answer 10

yes i did that then do i take point (p3-p2)?
p2-p1= (3,-7,-7)

Answer 11

now with (3,-7,-7) (this is a vector paralell to the line) write the equation of the line.

Then check is the point P3 satisfies the equation

Answer 12

the equation of the line would be
x=6+3t , y=9-7t , z=7-7t

Answer 13

i dont think i know how to check to see if p3 satisfy the equation ...

Answer 14

just match the x co-ordinate and find a value for t
P3 has x=0
that means t=-2

but when t=-2
y=23
z=21

so P3 is not a point on the line

Answer 15

o ok thanks i understand now

Answer 16

come to think of it... there are easier methods to do this

Answer 17

there is? please share it ...hanks

Answer 18

have you learnt the "cross product"?

Answer 19

yes

Answer 20

take the vectors (P2-P1) and(P3-P1)
take their cross product, if they are parallel, it will be zero

Answer 21

if those two vectors are parallel, then the three points lie on the same line

Answer 22

p2-p1=(3,-7,-7)
p3-p1=(-6,-14,-10)
cross product . i(70-98)-j(-30-42)+k(-42-42)
=-28i+72j-84k

Answer 23

yep, so same conclusion, they dont lie on the same line

Answer 24

ok thanks

Answer 25

:)