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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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Show that the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) " and " (x-4)/(5)=(y-1)/(2)=z intersect each other . Find their point of intersection.

The distance of the point P(-2, 3, -4) from the line (x+2)/(3)=(2y+3)/(4)=(3z+4)/(5) measured parallel to the plane 4x+12y-3z+1=0 is d, then find the value of (2d-8), is……..

Knowledge Check

  • The sine of the angle between the line (x-2)/(3) = (y-3)/(4) = (z-4)/(5) and the plane 2x-2y+z=5 is

    A
    `(10)/(6 sqrt5)`
    B
    `(4)/( 5 sqrt2)`
    C
    `(2 sqrt3)/(5)`
    D
    `( sqrt2)/(10)`

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