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The position vector of two points A and ...

The position vector of two points A and B are `6vec(a) + 2vec(b) ` and `vec(a) - vec(b)`. If a point C divides AB in the ratio 3:2 then shown that the position vector of C is `3vec(a) - vec(b)` .

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Knowledge Check

  • If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

    A
    ` vec a - vec b`
    B
    `vec b - 2 vec a `
    C
    `vec a - 3 vec b `
    D
    ` vec b`

  • The position vector of the point which divides the join of points 2vec(a)-3vec(b) and vec(a)+vec(b) in the ratio 3:1 is

    A
    `(3vec(a)-2vec(b))/(2)`
    B
    `(7vec(a)-8vec(b))/(4)`
    C
    `(3vec(a))/(4)`
    D
    `(5vec(a))/(4)`

  • If the position vector of these points are vec(a) -vec(b)+3 vec(c ), 2 vec(a)+3vec(b)-4 vec( c) ,-7 vec(b) + 10 vec(c ) , then the three points are

    A
    collinear
    B
    non-coplanar
    C
    non-collinear
    D
    none of these

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