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The position vectors of A and B are bar(...

The position vectors of A and B are `bar(a) and bar(b)` respectively. If C is a point on the line `bar(AB)` such that `bar(AC)=5bar(AB)` then find the position vector of C.

A

`5bar(b)-4bar(a)`

B

`5bar(b)+4bar(a)`

C

`4bar(b)-5bar(a)`

D

`4bar(b)+5bar(a)`

Text Solution

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The correct Answer is:
A
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Find the equation of the line parallel to the vector 2 bar(i) - bar(j) + 2 bar(k) and which passes through the point A whose position vector is 3 bar(i) + bar(j) - bar(k) . If P is a point on this line such that AP = 15, find the position vector of P .

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Knowledge Check

  • The position vectors A, B are bar(a), bar(b) respectively. The position vector of C is (5bar(a))/3-bar(b) . Then

    A
    C is outside the `DeltaOAB` but inside the angle OBA
    B
    C is outside the `DeltaOAB` but inside the angle BOA
    C
    C is outside the `DeltaOAB` but inside the angle COA
    D
    inside the triangle OAB

  • If the position vectors of A, B are 2a + 3b - c, 4a - b + 5c, then the position vector of midpoint of bar(AB) is

    A
    3a + b + 2c
    B
    3a - b + 2c
    C
    3a + b - 2c
    D
    3a - b - 2c

  • Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are bar(a), bar(b), bar(c) and (bar(a)+bar(b)+bar(c))/4 respectively, then the position vector of the orthocentre of this triangle is

    A
    `-((bar(a)+bar(b)+bar(c))/2)`
    B
    `bar(a)+bar(b)+bar(c)`
    C
    `(bar(a)+bar(b)+bar(c))/2`
    D
    `bar(0)`

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    Let A, B, C, D be four points with position vectors bar(a) + 2 bar(b) , 2 bar(a) - bar(b) , bar(a) and 3 bar(a) + bar(b) respectively . Express the vectors bar(AC), bar(DA), bar(BA) and bar(BC) interms of bar(a) and bar(b)

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