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Show that the vector area of the triangl...

Show that the vector area of the triangle whosse vertices have position vector `veca,vecb,vecc` is `1/2(vecaxxvecb+vecbxxvecc+veccxxveca)`.

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Find the area of triangle whose vertices are (1,2), (3,4),(1/2,1/4).

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  2. Solve the following differential equations (dy)/(dx)+(y)/(x)=x^(2), ...

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  3. Show that the vector area of the triangle whosse vertices have positio...

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  4. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  5. Find the co-ordinates of the point where the line joining (3,4,-5) and...

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  6. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  7. Find the direction cosines of the line which is perpendicular to the l...

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  8. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

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  9. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  10. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  11. Find the points on the curve y = x^2+1 which are nearest to the point ...

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  12. Evaluate int0^ pi x/(1+ sin x) dx

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  13. Find the area of the regions into which the circle x^2+y^2=4 is divide...

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  14. Find the solution of the following differential equations: x dy-ydx=sq...

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  15. Show that hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) ...

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  16. A variable plane meets the coordinate axes at P, Q, R points. If the p...

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  17. Write whether the following statements are true or false. The equati...

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  18. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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  19. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  20. If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?

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