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Let L be the line of intersection of t...

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

Text Solution

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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

  • If the plane 2x-3y+6z=11 makes an angle sin^(-1) (alpha) with the x-axis , then the value of alpha is

    A
    `(sqrt3)/(2)`
    B
    `(2)/( sqrt3)`
    C
    `(1)/(7)`
    D
    `(2)/(7)`

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