- #1

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- Homework Statement
- See attached

- Relevant Equations
- Vectors

My interest is only on part (b),

For part (i), My approach is as follows,

##PB=PO+OB##

##PB=-\dfrac{2}{5}a +b##

##AD=AO+OD##

##AD=-a+\dfrac{5}{2}b##

Therefore, ##PB=\dfrac{2}{5}AD##

For part (ii), we shall have;

##QD=QB+BD##

##QD=\dfrac{2}{7}AB+\dfrac{3}{2}b##

##QD=-\dfrac{2}{7}a+\dfrac{2}{7}b+\dfrac{3}{2}b##

##QD=\dfrac{25}{14}b-\dfrac{2}{7}a##

also,

##PQ=PA+AQ##

##PQ=\dfrac{3}{5}a-\dfrac{5}{7}a+\dfrac{5}{7}b##

##PQ=\dfrac{5}{7}b-\dfrac{4}{35}a##

Therefore,

##PQ=\dfrac{1}{7}\left[5b-\dfrac{4}{5}a\right]##

&

##QD=\dfrac{1}{7}\left[\dfrac{25}{2}b-2a\right]##

It follows that,

##PQ=\dfrac{5}{7}\left[25b-4a\right]##

##QD=\dfrac{2}{7}\left[25b-4a\right]##

##OQ=\dfrac{2}{5} PQ## thus shown as there is a scalar connecting the two...seeking any alternative approach and i hope my working is correct as i do not have solutions to these questions...

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