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Consider the set of eight vector V={a ha...

Consider the set of eight vector `V={a hat i+b hat j+c hat k ; a ,bc in {-1,1}}dot` Three non-coplanar vectors can be chosen from `V` is `2^p` ways. Then `p` is_______.

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The correct Answer is:
`= 5`
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Knowledge Check

  • Given, two vectors are hat(i)-hat(j) and hat(i)+2hat(j) , the unit vector coplanar with the two vectors and perpendicular to first is

    A
    `(1)/(sqrt(2))(hat(i)+hat(j))`
    B
    `(1)/(sqrt(5))(2hat(i)+hat(j))`
    C
    `+-(1)/(sqrt(2))(hat(i)+hat(j))`
    D
    None of these

  • Two vectors P=2hat I +bhat j +2hat k and Q=hat i+hat j+hat k will be parallel if :

    A
    b=0
    B
    b=1
    C
    b=2
    D
    b=-4

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