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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Elnino_Gerrard on October 28, 2010, 05:09:47 pm

Title: Co planar?
Post by: Elnino_Gerrard on October 28, 2010, 05:09:47 pm: So i have 2 vectors a and b all i have to do is prove a=kb for co planar?
How about 3 vectors?
Title: Re: Co planar?
Post by: 98.40_for_sure on October 28, 2010, 05:11:35 pm: Isn't... coplanar mean same plane? a=kb is proving that they are parallel
Title: Re: Co planar?
Post by: jasoN- on October 28, 2010, 05:11:54 pm: what's co planar? is it co linear?
if it is colinear, then for example you had 3 position vectors OA, OB, OC
need to show that AB = kBC
and that both vectors share a common point (ie. B for the above example)
Title: Re: Co planar?
Post by: Elnino_Gerrard on October 28, 2010, 05:15:12 pm: Yea my bad i think i meant co- linear
Title: Re: Co planar?
Post by: Elnino_Gerrard on October 28, 2010, 05:15:46 pm: Quote from: jasoN- on October 28, 2010, 05:11:54 pm
what's co planar? is it co linear?
if it is colinear, then for example you had 3 position vectors OA, OB, OC
need to show that AB = kBC
and that both vectors share a common point (ie. B for the above example)

Yep thats the answer i was looking for :P thanks mate :P
Title: Re: Co planar?
Post by: itolduso on October 28, 2010, 05:23:00 pm: how do you show a=2i-3j+k, b=5i-5j and c=i+j-2k are coplanar?
Title: Re: Co planar?
Post by: medge on October 28, 2010, 05:55:49 pm: Quote from: itolduso on October 28, 2010, 05:23:00 pm
how do you show a=2i-3j+k, b=5i-5j and c=i+j-2k are coplanar?

Quote

If three vectors $\mathbf{a}$ , $\mathbf{b}$ and $\mathbf{c}$ are coplanar, and $\mathbf{a}\cdot\mathbf{b} = 0$ , then

( $\mathbf{c}\cdot\mathbf{\hat a})\mathbf{\hat a} + (\mathbf{c}\cdot\mathbf{\hat b})\mathbf{\hat b} = \mathbf{c}$ ,

where $\mathbf{\hat a}$ denotes the unit vector in the direction of $\mathbf{a}$ .

Or, the vector resolutes of $\mathbf{c}$ on $\mathbf{a}$ and $\mathbf{c}$ on $\mathbf{b}$ add to give the original $\mathbf{c}$ .

^ according to wikipedia. I don't recall that being part of the course though...
Title: Re: Co planar?
Post by: TrueTears on October 28, 2010, 06:08:20 pm: Quote from: Elnino_Gerrard on October 28, 2010, 05:09:47 pm
So i have 2 vectors a and b all i have to do is prove a=kb for co planar?
How about 3 vectors?
um this isn't in the spesh course... at least i hope not, if anyone is interested.

if 2 vectors, a and b, are coplanar then a x b = 0.

if their cross product is = 0 then that means they MUST lie in the same plane, or else they will get a orthogonal vector that is not 0 :)
Title: Re: Co planar?
Post by: itolduso on October 28, 2010, 07:10:36 pm: cross product is not in spesh
Title: Re: Co planar?
Post by: TrueTears on October 28, 2010, 07:12:03 pm: thought so, i wonder why he/she asked this q lol
Title: Re: Co planar?
Post by: itolduso on October 28, 2010, 07:17:40 pm: Quote from: Elnino_Gerrard on October 28, 2010, 05:09:47 pm
So i have 2 vectors a and b all i have to do is prove a=kb for co planar?
How about 3 vectors?

Any two vectors with a common point are always coplanar. You dont have to show it.
Three vectors are coplanar if they are linearly dependent and have a common point. No cross product is necessary.