The value of `alpha` for which the system of linear equations: `x+(sin alpha)y+(cos alpha)z=0,x+(cos alpha)y+(sin alpha)z=0,-x+(sin alpha)y+(-cos alpha)z=0` has a non - trivial solution could be

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

Let lambda and alpha be real. Find the set of all values of lambda for which the system of linear equations lambdax + ("sin"alpha)y + ("cos" alpha)z =0 , x + ("cos"alpha)y + ("sin" alpha) z =0 and -x + ("sin" alpha)y -("cos" alpha)z =0 has a non-trivial solution. For lambda =1 , find all values of alpha .

Let lambda and alpha be real.Find the set of all values of lambda for which the system of linear equations lambda x+(sin alpha)y+(cos alpha)z=0,x+(cos alpha)y+(sin alpha)z=0,quad -x+(sin alpha)y-(cos alpha)z=0

The number of values of alpha in [-10pi, 10pi] for which the equations (sin alpha)x-(cos alpha)y+3z=0, (cos alpha)x+(sin alpha)y-2z=0 and 2x+3y+(cos alpha)z=0 have nontrivial solution is

If system of equations (tan alpha)x+(cot alpha)y+(8cos2 alpha)z=0

If x=a sin alpha+b cos alpha and y=a cos alpha-b sin alpha then remove alpha