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The points D, E, F divide BC, CA and AB...

The points `D, E, F` divide `BC, CA and AB` of the triangle ABC in the ratio `1:4,3:2 and 3:7` respectively and the point divides AB in the ratio `1:3`, then `(bar(AD) +bar(BE) + bar(CF)): bar(CK)` is equal to

A

`1:1`

B

`2:5`

C

`5:2`

D

none of these

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • ABC is a triangle , D, E, F are points in the sides BC, CA, AB respectively dividing them in the ratio 1 : 4, 3 : 2 and 3 : 7 respectively. The point P divides AB in the ratio 1 : 3 , then (vecAD + vecBE + vecCF) : vecCP =

    A
    `1 : 1`
    B
    `2 : 5`
    C
    `5 : 2`
    D
    none

  • In triangleABC, if the points P, Q, R divides the sides BC, CA, AB in the ratio 1:4, 3:2, 3:7 respectively and the point S divides side AB in the ratio 1:3, then (overline(AP)+overline(BQ)+overline(CR)):(overline(CS)) =

    A
    `2:5`
    B
    `5:2`
    C
    `4:5`
    D
    `5:4`

  • If D is the mid -point of side AB of DeltaABC , then bar(AB) + bar(BC) + bar(AC) =

    A
    `2(bar(AD)-bar(BD))`
    B
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    C
    `2(bar(BD)-bar(CA))`
    D
    `2(bar(BD)-bar(AC))`

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