If the system of equation `x-(sin theta)y-z = 0, (sin theta)x-y-z = 0 and x + y-z = 0` has non zero solution then (where `pi in (0, pi))`

the value of theta for which the system of equations (sin 3theta)x-2y+3z=0, (cos 2theta)x+8y-7z=0 and 2x+14y-11z=0 has a non - trivial solution, is (here, n in Z )

the value of theta for which the system of equations (sin 3theta)x-2y+3z=0, (cos 2theta)x+8y-7z=0 and 2x+14y-11z=0 has a non - trivial solution, is (here, n in Z )

The system of equations (sin 3 theta) x - y+z=0,(cos 2 theta)x+4y+3z=0, 2x+7y+7z=0 has non trivial solutions if

If the system of equation : x + y + z = 0 , 2 x + 3y + 4z = 0 , kx + y - z = 0 has a non - zero solution , then the value of k is

If 0lt= thetalt=pi and the system of equations x+(sin theta)y- (costheta) z =0, (cos theta ) x-y+z=0, (sin theta) x+y-z=0 has a non -trivial solution then theta is

If the system of equations x-ky-z=0 , kx-y-z=0 , x+y-z=0 has a non-zero solution , then possible values of k are :

The system of equations ax + y + z = 0 , -x + ay + z = 0 and - x - y + az = 0 has a non-zero solution if the real value of 'a' is

If the system of equations x – ky – z = 0, kx – y – z=0, x + y – z = 0 has a non -zero solution then the possible values of k are