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Prove that d/(dx)|(u1,v1,w1),(u2,v2,w2),...

Prove that `d/(dx)|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_3,v_3,w_3)|=|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_4,v_4,w_4)|` where `u,v,w` are functions of `x and (du)/(dx)=u_1,(d^2u)/(dx^2)=u_2,` etc.

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Knowledge Check

  • The matrices P[(u_(1),v_(1),w_(1)),(u_(2),v_(2),w_(2)),(u_(3),v_(3)w_(3))] and Q=(1)/(9)[(2,2,1),(12,-5,m),(-8,1,5)] are such that PQ=l, an identify matrix. Solving the equation [(u_(1),v_(1),w_(1)),(u_(2),v_(2),w_(2)),(u_(3),v_(3),w_(3))][(x),(y),(z)]=[(1),(1),(5)] , the value of y comes out to be -3, then the value of m is equal to

    A
    27
    B
    7
    C
    `-27`
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    A
    `(4-3x^(2))/sqrt(3-2x^(2))`
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  • If u, v, w are unit vectors satisfying 2u+2v+2w=0," then "abs(u-v) equals

    A
    `7/4`
    B
    `sqrt(5/2)`
    C
    `sqrt(7/2)`
    D
    `5/4`

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