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Show that [veca+vecbvecb+veccvecc+veca] ...

Show that `[veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]`

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Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

Show that veca, vecb and vec c are coplanar if veca+vecb,vecb+vecc and vecc+veca are coplanar.

For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) . Interpret this result geometrically.

For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk , obtain vecaxx(vecbxxvecc) and also verify the formula vecaxx(vecbxxvecc) = (veca.vecc)vecb-(veca.vecb)vecc .

If veca, vecb, vecc are mutually perpendicular vectors of equal magnitude, show that veca+vecb+vecc is equally inclined to veca.vecb.vecc .

If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-vecb)^2 . [(veca+vecb)^2 means (veca+vecb).(veca+vecb) , so does (veca-vecb)^2 .]

If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc .

|veca| = |vecb| = veca = vecb .

Prove that the four points with position vectors 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+6vecc are coplanar.

SHARAM PUBLICATION-QUESTION PAPER 2018-EXERCISE
  1. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  2. From the differential equation whose general solution is y=asint+be^t.

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  3. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  4. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

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  5. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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

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

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  8. The position vectors of two points A and B are 3hati+hatj+2hatk and ha...

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  9. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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  10. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

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  11. Solve the following system of equations by the matrix inversion method...

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  12. Two cards are drawn successively with replacement from a well-shuffled...

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  13. By elementary operations, find A^(-1) for the following: A=[[1,1,0],[1...

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  14. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  15. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

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  16. Evaluate: int ((2cosx+7)/(4-sinx))dx

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

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  18. Find the area enclosed by y=4x-1 and y^(2)=2x.

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  19. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  20. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

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