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Show that |{:((b+c)^2,a^2,a^2),(b^2,(c...

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`|{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}|=2abc(a+b+c)^3`

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Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^2,(s-c)^2,c^2]] = 2s^3(s-a)(s-b)(s-c)

Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}| = |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

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

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the equation of the line through (-1,0,1) and perpendicular to th...

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  2. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  3. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  4. Prove the following by vector method. Altitudes of a triangle are conc...

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  5. Prove that the measure of the angle between two main diagonals of a cu...

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  6. Let f : R to R be defined by f(x)=3x+5. Show that f is bijective. Find...

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  7. Prove that tan (pi/4+1/2cos^(-1)""a/b)+tan(pi/4-1/2cos^(-1)""a /b)=(2b...

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  8. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

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  9. Find the extreme points of the following functions. Specify if the ext...

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  10. Show that f(x)=[3x+ 11] is discontinuous at x=-11/3

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  11. Find the solution of the following differential equations: (4x+6y+5)dx...

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  12. int0^pi(xdx)/(1+sinx)

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  13. Show that int0^pixInsinx=pi^2/2In1/2

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  14. If A is a 4xx5 matrix and B is a matrix such that A^(T)B and BA^(T) bo...

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  15. What is F’(x) if F(x)=int0^xe^(3t)cos4t dt ?

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  16. Find r if -501 in[r]5.

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  17. To which coordinate axis is the plane 2y – 5z=0 parallel ?

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  18. What does the solution set of the inequation 2x+ygt5 represents?

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  19. What is the value of int(d)/(dx)f(x)dx-(d)/(dx)intf(x)dx?

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  20. IF [{:(3,5,3),(2,4,2),(lamda,7,6):}] is a singular matrix, then write ...

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