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

Answer» `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
`a=c`
`3b= 3a`
so,`a=b=c`
`cos alpha = a/(sqrt(a^2 + b^2+ c^2))= a/sqrt(3a^2) = 1/sqrt3`
option 1 is correct


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