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Let A, B, C, D be four points with posit...

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

Text Solution

Verified by Experts

The correct Answer is:
`bar(b)-bar(a)`
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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)

If bar(a)=2bar(i)-bar(j)+bar(k), bar(b)=bar(i)-3bar(j)-5bar(k) , find the vector bar(c) such that bar(a), bar(b) and bar(c) form the sides of a triangle.

Knowledge Check

  • The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c) are

    A
    Collinear
    B
    Coplanar but non collinear
    C
    non coplanar
    D
    cannot be determined

  • The vectors 5bar(a)+6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c), 3bar(a)+20bar(b)+5bar(c) are

    A
    Collinear
    B
    Coplanar but non collinear
    C
    non coplanar
    D
    cannot be determined

  • If the position vectors of the four points A, B, C, D are 2bar(a), bar(b), 6bar(b) and 2bar(a)+5bar(b) then ABCD is

    A
    square
    B
    rectangle
    C
    rhombus
    D
    parallelogram

    • Similar Questions

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    If bar(a) = bar(i) - bar(j)-bar(k), bar(b) = 2bar(i) - 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.

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