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Let L be the line of intersection of ...

Let L be the line of intersection of the planes `2x""+""3y""+""z""=""1` and `x""+""3y""+""2z""=""2` . If L makes an angles ` alpha `with the positive x-axis, then cos` alpha ` equals

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`P_1 = 2x+3y + z = 1`
`P_2 = x+ 3y + 2z = 2`
Dr of line`_|_`to `P_1 = (2,3,1)`
Dr of line`_|_`to `P_2 = (1,3,2)`
Dr of line L=`(a,b,c)`
`L _|_ P_1, 2a+ 3b + c = 0` (1)
`L _|_ P_2, a+ 3b+2c= 0` (2)
subtracting eqn 2 from 1
...
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Knowledge Check

  • Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle alpha with the positive X-axis, then cos alpha is equal to

    A
    `1//2`
    B
    1
    C
    `1//sqrt(2)`
    D
    `1//sqrt(3)`

  • Let be the line of intersection of the planes 2x+3y +z=1 and x+3y+2z =2 . If L makes an angle alpha with the positive x-axis, then cos alpha is equal to

    A
    `(1)/(2)`
    B
    1
    C
    `(1)/(sqrt(2))`
    D
    `(1)/(sqrt(3))`

  • Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2 . If L maker o angle alpha with the positive x-axis, then cos alpha equals :

    A
    `1/sqrt(3)`
    B
    `1/2`
    C
    1
    D
    `1/sqrt2`
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