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
Hello smmmcI'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 $\displaystyle \vec{BF}=\vec{OD} = \vec{i}$ and $\displaystyle \vec{CB}=\vec{OA}=3\vec{j}$
$\displaystyle \Rightarrow \vec{BN}=\tfrac12\vec{BF}=\tfrac12\vec{i}$
$\displaystyle \Rightarrow \vec{ON} = \vec{OC}+\vec{CB}+\vec{BN}$
$\displaystyle = 2\vec{k}+3\vec{j}+\tfrac12\vec{i}$
Also $\displaystyle \vec{OE} = \vec{OD}+\vec{DE} = \vec{i}+3\vec{j}$
$\displaystyle \Rightarrow \vec{OM} = \tfrac13\vec{OE}=\tfrac13\vec{i} + \vec{j}$
Now $\displaystyle \vec{ON}=\vec{OM}+\vec{MN}$
$\displaystyle \Rightarrow \vec{MN} = \vec{ON}-\vec{OM}$
$\displaystyle = 2\vec{k}+3\vec{j}+\tfrac12\vec{i}-\tfrac13\vec{i} - \vec{j}$
$\displaystyle =\tfrac16\vec{i}+2\vec{j}+2\vec{k}$
Grandad