Question

how is [7,5,3] coplanar to [1,1,1] and [1,2,3]? thanks

Answer 1

they are vectors btw

Answer 2

define the plane .....

Answer 3

cross 2 vectors to get the normal, then anchor it to one of the points .... tada, an equation to play with

Answer 4

If your matrices are up to speed, you can just GJ-Reduce and find the linear combination that you need for proof.

Answer 5

does it start like this:
1=s1
1=s2
1=s3
?

Answer 6

not sure what s1s2s3 refer to

Answer 7

have you gone over plane equations? or at best a dot product?

Answer 8

[1,1,1]=s[1,2,3]

Answer 9

thats not planar, thats parallel

Answer 10

if they are coplanar, then there is one vector that will be perpendicular to all of them, let that vector be (a,b,c) and apply the dot product

7a+5b+3c=0
1a,+1b+1c=0
1a+2b+3c=0

a system of 3 equations in 3 unknowns like in any basic algebra class.

Answer 11

here is the original question ... i actually got it wrong in a quiz but i only want to know how to solve it thats all

Answer 12

well, there is still going to be some trial and error, but in this case i would develop the plane equation to test out the options, and not the matrix solutions

Answer 13

tell me what you know of creating an equation of a plane from 2 vectors

Answer 14

hmm.. getting confused

Answer 15

the matrix process would create an infinite number of vectors as solution .... so thats not the route i would follow.

what do you know about creating a plane equation?

Answer 16

spose we define all the vectors that we can make from one of our given point, say from (1,1,1):

the vector from (1,1,1) to some point (x,y,z) is just subtraction: (x-1,y-1,z-1)

but this is all the vectors in a 3d space, we want to narrow them down to a plane .... using some vector (a,b,c) dotted to the vectors found, give us all the vectors that are perp to (a,b,c)

a(x-1)+b(y-1)+c(z-1) = 0

finding that vector (a,b,c) is the key to developing the equation we need.

Answer 17

it just so happens that finding the cross product of 2 vectors, defines a vector that is perp to both of them ... so we need to take the 2 given vectors, and cross them to find (a,b,c)