The sum of all possible values of θ [0, 2π], for which the system of equations: x cos 3θ-8y-12z=0, x cos 2θ+3y+3z=0, x+y+3z=0 has a non-trivial solution, is equal to:

Matrices and Determinants: JEE Main 2026 Mathematics question

JEE Main 2026 · 6 Apr, Evening shift · Q4

JEE Main 20266 Apr, Evening shiftMathematicsEasyMatrices and Determinants245× since 2002

The sum of all possible values of

\theta \in [0, 2\pi]

, for which the system of equations :

x\cos 3\theta-8y-12z=0

x\cos 2\theta+3y+3z=0

x+y+3z=0

has a non-trivial solution, is equal to :

JEE Main 2026 · 6 Apr, Evening shift · Q4

JEE Main 20266 Apr, Evening shiftMathematicsEasyMatrices and Determinants245× since 2002

The sum of all possible values of

\theta \in [0, 2\pi]

, for which the system of equations :

x\cos 3\theta-8y-12z=0

x\cos 2\theta+3y+3z=0

x+y+3z=0

has a non-trivial solution, is equal to :