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Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b...

Show that: `|3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot`

A

`3(a+b+c)(bc+ca+ab)`

B

`a+b+c`

C

`3(a+b+c)(a^(2)+b^(2)+c^(2))`

D

0

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The correct Answer is:
A
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3a,-a+b,-a+ca-b,3b,c-ba-b,3b,c-ba-c,b-c,3c]|=

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MCGROW HILL PUBLICATION-DETERMINANTS-EXERCISE (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. Suppose a,b,c in R and a+b+c!=0. Let Delta=|(b+c,c+a,a+b),(c+a,a+b,b+c...

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  2. Distance of line y=|(x+1,x,x),(x,x+2,x),(x,x,x+3)| from the origin ...

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  3. Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

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  4. If p,q and r are in AP the value of determinant |{:(a^(2)+2^(n+1)+2p,b...

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  5. Suppose a, b, c, d, e and f are in G.P with common ratio > 1. Let p. ...

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  6. Suppose pont (x,y,z) in space satisfies the equation |(x^(2)+1,xy,xz...

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  7. If A,B and C are angles of a triangle then the determinant |(-1,cosC...

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  8. Let Delta=|(a,x,x),(x,b,x),(x,x,c)| and f(x)=(x-a)(x-b)(x-c) Det...

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  9. Straight line |(2-x-y,4,4),(2x,x-y-2,2x),(2y,2y,y-2-x)|=0 passes t...

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  10. Suppose a in R. Let f(x)=|(x+a,x,x),(x,x+a,x),(x,x,x+a)|then f(2 x)-f(...

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  11. If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0, then th...

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  12. If alpha,beta & gamma are the roots the equations x^(3)+px+q=0 then th...

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

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  14. The determinant Delta =|(lamda a , lamda^(2)+a^(2),1),(lamda b,lamda^(...

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  15. If alpha,beta,gamma are real numbers, then determinant Delta=|(sin^2 a...

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  16. If bc+ca+ab=18 and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))...

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  17. If x!=0 the determinant Delta=|(a(0),a(1),a(2)),(-x,x,0),(0,-x,x)| ...

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  18. If x epsilon R the determinant Delta=|(1,cosx,0),(-1,1-cosx,sinx+cos...

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  19. The factors of |(x,a,b),(a,x,b),(a,b,x)|, are

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  20. Find the maximum value of |1 1 1 1 1+sintheta1 1 1 1+costheta|

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