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Prove that [vec(a)+vec(b),vec(b)+vec( c)...

Prove that `[vec(a)+vec(b),vec(b)+vec( c) , vec( c) +vec(a)] =2 [vec(a),vec(b),vec(c )]`.

Answer

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Prove that [vec(a),vec(b),vec( c) +vec(d)]=[vec(a),vec(b),vec( c)] +[vec(a),vec(b),vec(d)] .

Three vectors overline(a),overline(b) and overline(c) satisfy the condition vec(a)+vec(b)+vec(c)=vec(0) evaluate mu=vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a) if |vec(a)|=1,|vec(b)|=4 and |vec(c)|=2

Knowledge Check

  • (vec b xx vec c) xx (vec c xx vec a ) =

    A
    `[vec a vec b vec c]vec c`
    B
    `[vec a vec b vec c] vec b`
    C
    `[vec a vec b vec c]vec a`
    D
    `vec a xx (vec b xx vec c)`

  • (vec a - vec b).[(vec b - vec c) xx (vec c - vec a)] =

    A
    `2[vec a vec b vec c]`
    B
    `3[vec a vec b vec c]`
    C
    0
    D
    none of these

  • The value of [vec(a)-vec(b) vec(b)-vec(c) vec(c)-vec(a)] is equal to

    A
    0
    B
    1
    C
    `2[vec(a)vec(b)vec(c)]`
    D
    2

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    If vec(a), vec(b)" and "vec(c) are three unit vectors such that vec(a)+vec(b)+vec(c)=vec(O) , find the value of vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a) .

    If vec(a) = 2hat(i) - 3hat(j) + 4hat(k), vec(b) = hat(i) + 2hat(j) - 3hat(k) and vec(c ) = 3hat(i) + 4hat(j) - hat(k) , then find vec(a).(vec(b) xx vec(c )) and (vec(a) xx vec(b)).vec(c ) . Is, vec(a).(vec(b) xx vec(c )) = (vec(a) xx vec(b)).vec(c ) ?

    If vec(a) = 3vec(i) - 2vec(j) + 2vec(i), vec(b) = 6vec(i) + 4vec(j) - 2vec(k), vec(c ) = 3hat(i) - 2hat(j) - 4hat(k) , Then vec(a).(vec(b) xx vec(c )) is

    If vec(a), vec(b), vec(c ) are unit vectors such that vec(a) + vec(b) + vec(c )= vec(0), " then " vec(a).vec(b) + vec(b).vec(c ) + vec(c ).vec(a) =

    If [vec(a),vec(b),vec(c)] denotes the scalar triple product of the vectors vec(a),vec(b),vec(c) , then [vec(a)+vec(b),vec(b)+vec(c),vec(c)+vec(a)] is equal to

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