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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-MODEL QUESTION PAPER 19-EXERCISE
  1. If [[x+y,x-2],[2x-z,0]]=[[2,5],[3,1]] then the values of x,y,z.

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  2. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

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  3. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

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  4. If A=[[2,1],[-1,3]] B=[[2,5],[-3,2]] find AB and BA.

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  5. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  6. Find a vector of magnitude 5 units and parallel to the resultant of ve...

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

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  8. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  9. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

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  10. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  11. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  12. [[2,5],[3,4]][[3,1],[-2,3]]=[[x,y],[1,z]] find x,y and z.

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  13. Using properties of determinants, prove the following abs{:(a^2, bc, a...

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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 tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  16. int(pi//6)^(pi//3)dx/(1+sqrtcotx)

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  17. Using integration, find the area bounded by the curve x^2 = 4y and the...

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  18. Solve the differential equation (x^(2)+1)(dy)/(dx)+2xy= sqrt(x^(2)+4),

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  19. Find a unit vector perpendicular to both of the vectors veca + vecb an...

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  20. Find the vector and cartesian equations of the line passing through th...

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