Question

Pt. D divides BC in ratio 7:2

Pt. E divides AD in ratio 1:3

Find the ratio of
$\frac{∆ABC}{∆AEC}$


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Answer 1

Take A as origin and the position vectors of B and C be b and c. 

Hence the position vectors of other points under given conditions are 

D=53c+2b,E=41.0+3c=43c.

Equations of AD and BE are

AD is r=t53c+2b

BE is r=(1−s)b+s⋅43c.

They intersect at H. 

Comparing coefficients of b and c, we get 

52t=1−s,53t=43s.

∴s=54t.

∴52t+54t=1

∴t=65,s=64

Point H is 63c+2b.

Now