A line L is parallel to both the planes 2x+3y+z=1 and x+3y+2z=2. If line L makes an angle with the positive direction of X -axis, then cos ⁡ =

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Accepted Answer

Correct answer: A. (a) Line parallel to both planes will be perpendicular to normal vector of both planes which is =3i-3j+3k=3 (i-j+k ) (ijk231132 ) Angle with X axis = ∴ cos ⁡ = 3 3^2+ (-3 )^2+3^2= 33 3 ∴ cos ⁡ = 1 3 .

$A line L is parallel to both the planes 2 x + 3 y + z = 1 and x + 3 y + 2 z = 2 . If line L makes an angle α with the positive direction of X -axis, then cos α =$

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