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If vecp=frac[1][lambda](vecbtimesvecc),...

If ` vecp=frac[1][lambda](vecbtimesvecc),vecq=frac[1][lambda](vecctimesveca)` and `vecr=frac[1][lambda](vecatimesvecb)` where ` lambda=[vecavecbvecc]ne0` then show that ` (veca+vecb+vecc)cdot(vecp+vecq+vecr)=3`.

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USHA PUBLICATION-PREVIOUS YEAR QUESTION 2017-PREVIOUS YEAR QUESTION
  1. Prove that the vectors 2hati-hatj+hatk, hati-3hatj-5hatk, 3hati-4hatj-...

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  2. If veca=3hati+hatj+2hatk,vecb=2hati-3hatj+4hatk then verify that vecat...

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  3. If vecp=frac[1][lambda](vecbtimesvecc),vecq=frac[1][lambda](vecctimes...

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  4. Find the equation of the plane through the point (2,1,0) and passing t...

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  5. Find the co-ordinates of the point where the perpendicular from the or...

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  6. Find the value of a for which the plane x+y+z-a=0 will touch the spher...

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  7. Find the feasible region of the system. 2y-xge0,6y-3xle21,xge0,yge0

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  8. Solve the following LPP graphically: Maximize z=20x+30y subject to 3x+...

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  9. Solve by Cramer’s rule 2x-y=2, 3x+y=13

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  10. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  11. Find the inverse of the following matrix: [[0,0,2],[0,2,0],[2,0,0]]

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  12. If P(n-1,3):P(n+1,3)=5:12, find n.

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  13. A cricket team consisting of 11 players is to be chosen from 8 batsmen...

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  14. Write the principal value of sin^(-1)frac[1][2]+cos^(-1)(-frac[1][2])

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  15. Five boys and four girls randomly stand in a line. Find the probabilit...

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  16. If a random variable X has a binomial distribution B(8,frac[1][2]), th...

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  17. If (a + bx)e^(y/x) = x, then show that x^3d/dx (dy/dx) = (x dy/dx - ...

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  18. A cylindrical open water tank with a circular base is to be made out o...

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  19. Evaluate intfrac[dx][cosx(1+2sinx)]

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  20. Solve frac[dx][dy]=frac[3x-7y+7][3y-7x-3]

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