In triangle ABC, point D divides BC in ratio 1:4, point E divides CA in ratio 3:2, and point F divides AB in ratio 3:7. Point K divides AB in ratio 1:3. Find |AD + BE + CF|: |CK|.

1: 1
2: 5
5: 2
None of these

Correct answer: 2: 5

Solution

Using position vectors: AD + BE + CF = (3A+B-4C)/10 and CK = (3A+B-4C)/4. Hence |AD+BE+CF|:|CK| = (1/10):(1/4) = 4:10 = 2:5.

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