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

1. 1
2. 1/√2
3. 1/√3
4. 1/2

Correct answer: 1/√3

Solution

The angle α that line L makes with the positive x-axis can be determined using the direction ratios of the line, which are derived from the normal vectors of the intersecting planes. The cosine of the angle is calculated as the ratio of the x-component of the direction vector to the magnitude of the direction vector, resulting in cos α = 1/√3.

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