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If a^2+b^2+c^2=1, then prove that |[a^...

If `a^2+b^2+c^2=1,` then prove that `|[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ac(1−cosθ)],[ba(1−cosθ),b^2+(c^2+a^2)cosθ,bc(1−cosθ)],[ca(1−cosθ),cb(1−cosθ),c^2+(a^2+b^2)cosθ]|` independent of a,b,c?

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

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  2. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

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  3. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

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  4. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, a) There are ex...

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  5. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

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  6. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

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  7. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

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  8. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

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  9. If Dk=|[1, n, n];[ 2k, n^2+n+1, n^2+n];[ 2k-1, n^2, n^2+n+1]|a n...

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  10. If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p...

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  11. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

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  12. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

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  13. For a fixed positive integer n , if Delta=|[n !,(n+1)!,(n+2)!],[(n+1)!...

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  14. The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

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  15. if f(alpha,beta)=|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[co...

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  16. 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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  17. If (1+x+x^(2))^(25)=a(0)+a(1)x+a(2)x^(2)+...+a(50).x^(50), then a(0)+a...

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  18. Find the value of lambda for which the homogeneous system of equations...

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  19. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

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  20. Let a ,b ,c be positive and not all equal. Show that the value of the ...

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