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The position vectors of the three non-co...

The position vectors of the three non-collinear points A, B, C, are `bara, barb, barc` respectively. The distance of the origin from the plane through A, B, C is

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bara,barb,barc and bard are the position vectors of four coplanar points such that (bara-bard).(barb-barc)=(barb-bard).(barc-bara)=0 . Show that the point bard represents the orthocentre of the triangle with bara,barb and barc as its vertices.

Knowledge Check

  • If bara, barb and barc are three non-collinear points and kbara+2barb+3barc is a point in the plane of bara, barb,barc then k=

    A
    4
    B
    5
    C
    `-5`
    D
    `-4`

  • If a, b and c are three non-collinear points and ka+2b+3c is a point in the plane of a, b, c then k=

    A
    4
    B
    5
    C
    `-5`
    D
    `-4`

  • Let the position bartors of two points A and B be bara+barb+barc and bara-2barb+3barc respectively. If the points P and Q divide AB in the ratio 1:3 internally and externally respectively , then 3|bar(AB)| =

    A
    `4|bar(PQ)|`
    B
    `3|bar(PQ)|`
    C
    `1/2|bar(PQ)|`
    D
    `2|bar(PQ)|`

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    Assertion (A) : bara,barb,barc and bard are the position vectors of four coplanar points A, B, C, D. If abs(bard-bara)=abs(bard-barb) =abs(bard-barc) , then D is the circumcentre of Delta ABC Reason ( R ) : In any triangle, the circumcentre is equidistant from the vertice. Then

    If bara,barb,barc are the position vectors of the vertices of a triangle ABC, then the area of triangle ABC is

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    Let bara = 2 bari + barj - 3bark and barb = bari + 3barj + 2bark. then the volume of the parallelopiped having coterminous edge as bara, barb and barc, where barc is the vector perpendicular to the plane of bara, barb |barc| =2 is

    If bara,barb,barc " are three non zero vectors, and " bara.barb = bara.barc rArr

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