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Let the vectors vec(PQ),vec(QR),vec(RS),...

Let the vectors `vec(PQ),vec(QR),vec(RS), vec(ST), vec(TU)` and `vec(UP)` represent the sides of a regular hexagon.
Statement I:`vec(PQ) xx (vec(RS) + vec(ST)) ne vec0`
Statement II: `vec(PQ) xx vec(RS) = vec0` and `vec(PQ) xx vec(RS) = vec0` and `vec(PQ) xx vec(ST) ne vec0`
For the following question, choose the correct answer from the codes (A), (B) , (C) and (D) defined as follows:

Text Solution

Verified by Experts

The correct Answer is:
c
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Let three vectors vec(a), vec(b) and vec(c ) be such that vec(a) xx vec(b) = vec(c), vec(b) xx vec(c) = vec(a) and |vec(a)| = 2 . Then which one of the following is not true ?

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Knowledge Check

  • Let the vectors vec(PQ),vec(QR),vec(RS),vec(ST),vec(TU) and vec(UP) represent the sides of a regular hexagon. Statement 1: vec(PQ)xx(vec(RS)+vec(ST))!=vec0 Statement 2: vec(PQ)xxvec(RS)=vec0 and vec(PQ)xxvec(ST)!=vec0

    A
    1
    B
    2
    C
    3
    D
    4

  • If vec(a). vec(b) = 0 and vec(a) xx vec(b) = vec(0) then which one of the following is correct ?

    A
    `vec(a)` is parallel to `vec(b)`
    B
    `vec(a) ` is perpendicular to `vec(b)`
    C
    `vec(a)=vec(0) or vec(b)=vec(0)`
    D
    None of the above

  • If vec(a)xx vec(b) = vec(c) and vec(b) xx vec(c) = vec(a) , then which one of the following is correct?

    A
    `vec(a),vec(b),vec(c)` are orthogonal in pairs and `|vec(a)|=|vec(c)| and |vec(b)|=1`
    B
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    C
    `vec(a), vec(b), vec(c)` are orthogonal in pairs but `|vec(a)|!=|vec(c)|`
    D
    `vec(a), vec(b), vec(c)` are orthogonal is pairs but `|vec(b)|!=1`

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