vector problem

**smmmc** · September 16th 2009, 02:16 AM

Hey

OABCDEFG is a cuboid

-> -> ->
OA= 3j OC=2k OD=i

M is such that ->
OM= 1/3 ->
OE

N is the midpoint of BF. Find
a) ->
MN

not sure how to start, i drew a cuboid but dont know how to find the 1/3 of OE

thanks
Thanks

**Grandad** · September 16th 2009, 04:52 AM

Hello smmmc

Originally Posted by smmmc

Hey

OABCDEFG is a cuboid

-> -> ->
OA= 3j OC=2k OD=i

M is such that ->
OM= 1/3 ->
OE

N is the midpoint of BF. Find
a) ->
MN

not sure how to start, i drew a cuboid but dont know how to find the 1/3 of OE

thanks
Thanks

I'm assuming that the vertices are labelled as in the attached diagram, so that, for instance, BF is parallel to CG, OD and AE.

If this is the case, then $\vec{BF}=\vec{OD} = \vec{i}$ and $\vec{CB}=\vec{OA}=3\vec{j}$

$\Rightarrow \vec{BN}=\tfrac12\vec{BF}=\tfrac12\vec{i}$

$\Rightarrow \vec{ON} = \vec{OC}+\vec{CB}+\vec{BN}$

$= 2\vec{k}+3\vec{j}+\tfrac12\vec{i}$

Also $\vec{OE} = \vec{OD}+\vec{DE} = \vec{i}+3\vec{j}$

$\Rightarrow \vec{OM} = \tfrac13\vec{OE}=\tfrac13\vec{i} + \vec{j}$

Now $\vec{ON}=\vec{OM}+\vec{MN}$

$\Rightarrow \vec{MN} = \vec{ON}-\vec{OM}$

$= 2\vec{k}+3\vec{j}+\tfrac12\vec{i}-\tfrac13\vec{i} - \vec{j}$

$=\tfrac16\vec{i}+2\vec{j}+2\vec{k}$

Grandad

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