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If alpha,beta,gamma are the angles of a ...

If `alpha,beta,gamma` are the angles of a triangle and system of equations `cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0` `cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0` `sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0` has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled`""` d. acute angled

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. If A , Ba n dC are the angels of a triangle, show that |[-1+cos B, c...

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  3. If alpha,beta,gamma are the angles of a triangle and system of equatio...

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  4. Without expanding the determinants, prove that |(103, 115, 114), (111,...

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  5. Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z a...

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  6. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

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  7. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

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  8. Prove that the value of the determinant |[-7, 5+3i,2/3-4i], [5-3i,8, 4...

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  9. If the system of linear equation x+y+z=6,x+2y+3c=14 , and 2x+5y+lambda...

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  10. If ar=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a1,a2,a3],[a4,a5,a...

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  11. Let f(x)=|(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0)| ....

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  12. Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))=4a^2b^2c^2.

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  13. The number of positive integral solutions of the equation |(x^3+1,x^2y...

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  14. If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive...

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  15. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,...

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  16. Using properties of determinants, evaluate |[18, 40 ,89],[ 40 ,89, 198...

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  17. If A1,B1,C1, are respectively, the cofactors of the elements a1, b1,c...

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  18. Solve for x |x-2 2x-3 3x-4 x-4 2x-9 3x-16 x-8 2x-27 3x-64|...

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  19. If Delta1=|[x, b, b],[ a, x, b],[ a, a, x]| a n d Delta2=|[x, b],[ a, ...

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  20. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

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