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If the position vectors of three consecu...

If the position vectors of three consecutive vertices of any parallelogram are respectively `vec i+vec j+vec k, vec i +3vec j+ 5vec k, 7vec i +9vec j +11vec k` then the position vector of its fourth vertex is:

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Midpoint of AC= Midpoint of BD
`((1+7)/2,(1+9)/2,(1+11)/2)=((x+1)/2,(y+3)/2,(z+5)/2)`
`x=8-1=7`
`y=10-3=7`
`z=7`
`D(7,7,7)`
position vector of D=`7veci+7vecj+7veck`
`=7(veci+vecj+veck)`.
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