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length of `bar(AP)=3cm and bar(BP)=bar(AP)` in the figure. Then length of AB is?

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Length of bar(AP)=3 cm and AP=PB. Then what is the length of AB ?

In /_\ABC , D, E, F are the mid-points of bar(AB) , bar(BC) , bar(CA) and if bar(AB) = 11 cm, bar(BC) = 9 cm, bar(CA) = 8cm. Find the lengths of bar(DE) , bar(EF) and bar(DF) .

Knowledge Check

  • Let there be two points A, B on the curve y=x^(2) in the plane XOY satisfying bar(OA).bari =1 and bar(OB).bari = -2 then the length of the vector 2bar(OA)-3bar(OB)=

    A
    `2sqrt(41)`
    B
    `sqrt(41)`
    C
    `(sqrt(41))/(2)`
    D
    `sqrt(14)`

  • The vectors of bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4bar(k) are the sides of a triangle ABC. The length of the median through A is

    A
    `sqrt(72)`
    B
    `sqrt(33)`
    C
    `sqrt(288)`
    D
    `sqrt(18)`

  • If the diagonals of a parallelogram are given by 3bar(i)+bar(j)-2bar(k) and bar(i)-3bar(j)+4bar(k) then the length of its sides are

    A
    `sqrt(8), sqrt(10)`
    B
    `sqrt(6), sqrt(14)`
    C
    `sqrt(5), sqrt(12)`
    D
    `sqrt(3), sqrt(12)`

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    If the position vectors of the point A, B and C are - 2 bar(i) + bar(j) - bar(k), - 4 bar(i) + 2 bar(j) + 2 bar(k) and 6 bar(i) - 3 bar(j) - 13 bar(k) respectively and bar(AB) = lambda bar(AX) , then find the value of lambda

    In the parallelogram if bar(AB)=bar(a) and bar(AD)=bar(d) then find bar(BD) .

    The position vector of the points P, Q, R, S are bar(i)+bar(j)+bar(k), 2bar(i)+5bar(j), 3bar(i)+2bar(j)-3bar(k) and bar(i)-6bar(j)-bar(k) respectively. Prove that bar(PQ) and bar(RS) are parallel and find the ratio of their lengths.

    In DeltaOAB , L is the midpoint of OA and M is a point on OB such that (OM)/(MB)=2 . P is the mid point of LM and the line AP is produced to meet OB at Q. If bar(OA)=bar(a), bar(OB)=bar(b) then find vectors bar(OP) and bar(AP) interms of bar(a) and bar(b) .

    If the diagonals of a parallelogram are bar(i)+5bar(j)-2bar(k) and -2bar(i)+bar(j)+3bar(k) then the lengths of its sides are

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