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If vec a\ xx\ vec b=\ vec c\ xx\ vec...

If ` vec a\ xx\ vec b=\ vec c\ xx\ vec d\ ` and ` vec a\ xx\ vec c=\ vec b\ xx vec d` show that ` vec a- vec d` is parallel to ` vec b- vec c ,` where ` vec a!= vec d` and ` vec b!= vec c`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Differentiate the following function w.r.t. x : x^(sinx)+(sin x)^(...

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  2. If A is an invertible matrix of order 3\ and |A|=5, then find |a d...

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  3. If vec a\ xx\ vec b=\ vec c\ xx\ vec d\ and vec a\ xx\ vec c=\ ...

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  4. Find the value of lamda so that the lines (1-x)/(3)=(7y-14)/(2lamda)=(...

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  5. Solve the following differential equation: (dy)/(dx)+y=cosx-sinx

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  6. Find the particular solution, satisfying the given condition, for t...

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  7. By using properties of determinants, prove the following |(x+4,2x,2x),...

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  8. Write the vector equation of the following line: (x-5)/3=(y+4)/7=(6-z...

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  9. Using integration, find the area of the triangle ABC, coordinates o...

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  10. Find the area of circle 4x^2+4y^2=9 which is interior to the parabo...

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  11. If siny=sin(a+y),\ \ prove that (dy)/(dx)=(sin ^2\ (a+y))/(sina)

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  12. If (cos"x")^y=(sin y)^x , find (dy)/(dx)

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  13. Solve the following differential equation: ((x^2-1)dy)/(dx)+2x y=1/(x...

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  14. Solve the following differential equation: sqrt(1+x^2+y^2+x^2\ y^2)\ ...

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  15. If y=logtan(pi/4+x/2),\ show that (dy)/(dx)=secxdot Also find the ...

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  16. If y=cos^(-1)((2^x+1)/(1+4^x), find (dy)/(dx)

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  17. Evaluate : int0^pi(xtan\ x)/(sec\ x+tan\ x)\ dxdot

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  18. From the following matrix equation, find the value of x:[[x+y,4],[-5,...

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  19. Prove the following: tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)...

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  20. Form the differential equation representing the family of ellipses ...

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