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

Explanation

`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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