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Vectors vecm, vecn, vecr are such that v...

Vectors `vecm, vecn, vecr` are such that `vecm + vecn + vecr = 0`, prove that `vecm xx vecn = vecn xx vecr = vecr xx vecm`

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If veca, vecb, vecc and vecd are distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecb-vecc)ne 0

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If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

Let veca=-hati-hatk,vecb =-hati + hatj and vecc = i + 2hatj + 3hatk be three given vectors. If vecr is a vector such that vecr xx vecb = vecc xx vecb and vecr.veca =0 then find the value of vecr .vecb .

vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors and vec r is any vector in space, then ( veca × vecb )×( vecr × vecc )+( vecb × vecc )×( vecr × veca )+( vecc × veca )×( vecr × vecb ) is equal to

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If vecp xx vecq = vecm xx vec n and vecp xx vec m = vecq xx vecn , show that vecp- vecn is parallel to vecq - vecm where vecp ne vecn and vecq ne vecm .

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If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Solve(d^2y)/(dt^2) = tan y sec ^2 y, given dy/dt = 0 when y = 0

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  2. Prove that cos (sinx) > sin (cos x) for all x in 0 le x le pi//2

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  3. If the line ax+by+c=0 is a normal to the curve xy=1 then

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  4. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  5. Find the point on the curve 4x^2 + a2y^2 = 4a^2, 4 < a^2 < 8 that is f...

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  6. The area bounded by the parabola y = x - x^2 and the line y = mx equal...

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  7. Prove that f(x)= sin x+sqrt 3 cosx has maximum value at x=pi/6

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  8. The length of the hypotenuse of a right angled triangle is 3 ft. Find ...

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  9. The angle between the tangents to the curves y=sin x and y = cos x at ...

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  10. Show that f(x) = (x-2)e^x + x + 2 is positive for all positive values ...

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  11. Vectors vecm, vecn, vecr are such that vecm + vecn + vecr = 0, prove t...

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  12. If vecp xx vecq = vecm xx vec n and vecp xx vec m = vecq xx vecn, sho...

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  13. If veca xx vecb + vecb xx vecc + vecc xx veca = 0. Show that the vecto...

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  14. The vector vecr is collinear with vector vecn = 2hati + hatj + 3hatk ...

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  15. If veca,vecb and vecc are three mutually perpendicular vectors of equa...

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  16. Find the equation of the plane passing through the point(1,2,1) and pe...

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  17. Find the vector equation of the following plane in scalar product from...

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  18. two numbers are selected at random from 1,2,3,….., 100 and are multipl...

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  19. In a class, 5% of the boys and 10% of the girls have an IQ more than 1...

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  20. If P(A//C) geP(B//C) P(A//barC) geP(B//barC), then prove that, P(A)geP...

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