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Prove that (veca.vecb)^2=a^2b^2-(veca xx...

Prove that `(veca.vecb)^2=a^2b^2-(veca xx vecb)^2`

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Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2 .

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 .]

Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)

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

Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (veca xx vecb) = vec0 and hence prove that veca xx (vecb xx vecc), vecb xx (vecc xx veca), vecc xx (veca xx vecb) are coplanar.

If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbxxvecc)]^2 = a^2b^2c^2

What is the angle between veca and vecb if abs(veca+vecb)=abs(veca-vecb) ?

Prove that : |veca + vecb|le|veca|+|vecb| .

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

What is abs(veca-vecb)=if abs(veca)=3,abs(vecb)=4 and abs(veca+vecb)=5 ?

SHARAM PUBLICATION-MODEL QUESTION PAPER -16-EXERCISE
  1. Integrate :inttan^-1x/(1+x^2)dx

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  2. Evaluate int0^(pi/2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx

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  3. Find the area bounded by the line y = 2x, x- axis and the ordinate x =...

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  4. Solve 2y^3(dy)/(dx)=ax

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  5. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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  6. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  7. Write the volume of the parallelopiped whose sides are given by-hatj, ...

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  8. The angle between the plane 3x+3z-5=0 and the line (x-1)/1=(y-2)/-1=(z...

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  9. Find the equation of the plane passing through the intersection of the...

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  10. Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

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  11. Show that the lines (x-4)/1=(y+3)/-4=(z+1)/7 and (x-1)/2=(y+1)/-3=(z+1...

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

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  13. Find the altitude of a right circular cylinder of maximum volume inscr...

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  14. Evaluate the following integrals int(12sinx-2cosx+3)/(sinx+cosx)dx

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  15. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

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  16. Solve the following differential equations (dy)/(dx)+2ytan x= sin x,...

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  17. If A=[[1,1],[-1,-1]], B=[[-1,3],[-3,1]] then show that (A+B)^2 !=A^2 +...

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  18. If f:RrarrR defined by f(x)=5x-8 for all x inR, then show that f is in...

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  19. Prove statement "sin"^(-1) 3/5+ "cos"^(-1)12/13="cos"^(-1) 33/65

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  20. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

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