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If system of equations (tan alpha)x+(cot...

If system of equations `(tan alpha)x+(cot alpha)y+(8 cos 2 alpha)z=0`

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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

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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

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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

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+ (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 then S contains a) (-1,1) b) [-sqrt2,-1] c) [1,sqrt2] d) [-sqrt2,sqrt2]