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Evaluate ((2)/(3)x-(3)/(4)y+(4)/(5)z)^(2...

Evaluate `((2)/(3)x-(3)/(4)y+(4)/(5)z)^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
`(4)/(9)x^(2)+(9)/(16)y^(2)+(16)/(25)z^(2)-xy-(6)/(5)yz+(16)/(15)zx`
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Knowledge Check

  • The point of intersection of lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4)and(x-4)/(5)=(y-1)/(2)=(z)/(1) is

    A
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    B
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    C
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    D
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    A
    `cos^(-1)((108)/(sqrt11990))`
    B
    `cos^(-1)((99)/(sqrt9701))`
    C
    `cos^(-1)((9)/(sqrt9701))`
    D
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  • (x^(4))/(4) + (y^(3))/(3) - (3z^(2))/(5) + (x^(4))/(3) - (3y^(3))/(5) + (z^(2))/(4) - (3x^(4))/(5) + (y^(3))/(4) + (z^(2))/(3) = "________" .

    A
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    B
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    C
    `(x^(4) + y^(3) + z^(2))/(60)`
    D
    `(x^(4) + y^(3) - z^(2))/(60)`

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