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If 0 lt theta lt pi and the system of eq...

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

A

`(pi)/(6)`

B

`(pi)/(4)`

C

`(pi)/(3)`

D

`(pi)/(2)`

Text Solution

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The correct Answer is:
D
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  3. If 0 lt theta lt pi and the system of equations (sin theta) x + y + ...

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  4. If the determinant |(b -c,c -a,a -b),(b' -c',c' -a',a' -b'),(b'' -c'',...

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  5. If a !=b, then the system of equation ax + by + bz = 0 bx + ay + bz ...

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  6. If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+...

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  7. Show that a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0 are perpendicular to...

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  8. One factor of |(a^(2) + x,ab,ac),(ab,b^(2) + x,cb),(ca,cb,c^(2) + x)|,...

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  9. The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are ...

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  10. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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  11. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  12. The value of the determinant |k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1|...

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  13. The system of simulataneous equations kx + 2y -z = 1 (k -1) y -2z ...

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  14. The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,ome...

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  15. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  16. If the system of equations x + ay + az = 0 bx + y + bz = 0 cx + ...

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  17. The value of the determinant Delta = |(cos (alpha + beta),- sin (alp...

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  18. If omega is a cube root of unity, then for polynomila is |(x + 1,ome...

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  19. If Delta1=|[x,b,b],[a,x,b],[a,a,x]| and Delta2=|[x,b],[a,x]| are give...

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  20. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

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