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If the system of equations x + (√2 sin α)y + (√2 cos α)z = 0 x + (cos α)y + (sin α)z = 0 x + (sin α)y − (cos α)z = 0 has a non-trivial solution, then α ∈ (0, π/2) is equal to-

1. 3π/4
2. 7π/24
3. 5π/24
4. 11π/24

Correct answer: 5π/24

Solution

The system of equations has a non-trivial solution if the determinant of the coefficient matrix is zero. By calculating the determinant and setting it to zero, we find that α must equal 5π/24 to satisfy this condition.

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