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Find the direction ratios of a line normal to the plane passing through the points (1, 0, 0) and (0, 1, 0), if this plane makes an angle of π/4 with the plane x + y = 3.

1. 1, √2, 1
2. 1, 1, √2
3. 1, 1, 2
4. √2, 1, 1

Correct answer: 1, 1, √2

Solution

The correct option represents the direction ratios of the normal vector to the plane formed by the given points, which is orthogonal to the plane defined by the equation x + y = 3. The angle of π/4 indicates a specific relationship between the normals of the two planes, leading to the conclusion that the direction ratios must satisfy this geometric condition.

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