If `x,y,z` are not all simultaneously equal to zero, satisfying the system of `(sin 3theta)x-y+z=0 and (cos 2theta)x+4y+3z=0,` then the number of principal values of `theta` is

If x,y,z are not all simultaneously equal to zero, satisfying the system of (sin3 theta)x-y+z=0 and (cos2 theta)x+4y+3z=0 then the number of principal values of theta is

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

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 )

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 linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

Number of values of theta lying I [0,100 pi ] for which 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 solution is "____"

Number of values of theta lying I [0,100 pi ] for which 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 solution is "____"

Find the value theta for which the homogeneous system of equations: (sin 3 theta) x-y+z=0 , (cos2theta) x+4y+3z=0 and 2x+7y+7z=0 has non-trivial solutions.