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Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a...

Show that `|(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc`.

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Show that |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3) .

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|

Without expanding the determinant show that |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2|(a,b,c),(b,c,a),(c,a,b)|

Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

If abc!=0 and if |(a,b,c),(b,c,a),(c,a,b)|=0 then (a^(3)+b^(3)+c^(3))/(abc)=

Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-b)(b-c)(c-a)

SRISIRI PUBLICATION-QUESTION PAPER -Section B
  1. S.T |(1,a,a^2),(1,b,b^2),(1,c,c^2)| = (a-b)(b-c)(c-a).

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  2. Without expanding the determinant , prove that |{:(a,a^2,bc),(b,b^2,ca...

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  3. Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc.

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  4. If diagA=[a(1),a(2),a(3)], then for any integer n ge 1 show that A^(n)...

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  5. If ABCDEF is a regular hexagon with centre O , then P.T bar(AB)+bar(A...

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  6. If the points whose position vectors are 3bar(i) -2bar(j)-bar(k), 2bar...

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  7. Find the vector equation of the plane passing through the points. 4bar...

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  8. In the two dimensional plane, prove by using vector methods, the equat...

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  9. If bara,barb,barc are non-coplaner, then show that the vectors bara -b...

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  10. Find the area of the triangle formed with the points A(1,2,3), B(2,3,1...

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  11. If bar(a)=2bar(i)+bar(j)-bar(k), bar(b)=-bar(i)+2bar(j)-4bar(k), bar(c...

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  12. Prove that angle in a semi circle is a rightangle by using Vector meth...

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  13. If (sin(alpha+beta))/(sin(alpha-beta)) = (a+b)/(a-b), then prove that ...

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  14. Show that sin A= (sin 3A) /(1+2 cos 2A). Hence find the value of sin 1...

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  15. Show that 1/(sin 10^(@)) - (sqrt(3))/(cos 10^(@)) = 4.

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  16. Show that sin ^(4). (pi)/(8)+ sin ^(4) .(3pi)/(8) sin ^(4). (5pi)/(8)...

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  17. Prove that (1+cos""pi/10)(1+cos""(3pi)/10)(1+cos""(7pi)/10)(1+cos""(9p...

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  18. If cos alpha =(3)/(5) and cos beta =(5)/(13) and alpha, beta are acut...

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  19. If cos alpha =(3)/(5) and cos beta =(5)/(13) and alpha, beta are acut...

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  20. If alpha,beta are the solutions of the equation acostheta+bsintheta=c...

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