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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.

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. intdx/(sqrtx-root(3)(x))(x=t^6)

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  2. Find the co-ordinates of the foot of the perpendicular from the point ...

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

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  4. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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  5. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  6. Using vector method prove that cosA=(b^2+c^2-a^2)/(2bc)

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  7. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  8. Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2

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  9. In any triangle ABC, prove by vector method that frac[a][sinA]=frac[b]...

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  10. Find the distance of the point (3,-4,5)from the plane 2x+5y-6z-19=0 me...

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  11. Prove that the two lines whose direction cosines are connected by the ...

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  12. Integrate the following inte^(cos^2x)sin2x dx

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  13. Solve the differential equation (dy)/(dx)= (y-x+1)/(y+x+5).

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  14. Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1 /2)

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  15. If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)), then fin...

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

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  17. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  18. Minimize:Z=20x1+10x2 "Subject to": x1+2x2 le 40 3x1 -x2 ge 30 4x1+3x2 ...

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  19. If y=x sin^-1x+xcos^-1x, then what is dy/dx?

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  20. Give an example of a relation which is symmetric and anti-symmetric.

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