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

$fraction numerator 1 over denominator square root of 3 end fraction$

1/2

1

$fraction numerator 1 over denominator square root of 2 end fraction$

Solution

fraction numerator 1 over denominator square root of 3 end fraction

If direction cosines of L be l, m, n, then
2l + 3m + n = 0
l + 3m + 2n = 0
$solving comma space we space get comma space straight l over 3 space equals space fraction numerator straight m over denominator negative 3 end fraction space equals space straight n over 3 therefore space straight l colon straight m colon straight n space equals space fraction numerator 1 over denominator square root of 3 end fraction colon fraction numerator 1 over denominator square root of 3 end fraction colon fraction numerator 1 over denominator square root of 3 end fraction rightwards double arrow space space cos space straight alpha space equals space fraction numerator 1 over denominator square root of 3 end fraction$

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Three Dimensional Geometry

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