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

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

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

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

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

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

Find veca*(vecaxxvecb).

If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and veca.vecb = 6, find |veca+vecb| and |veca-vecb| .

Find a vector vecb such that vecaxxvecb=vecc and veca.vecb = 3 where veca = hati + hatj+hatk , vecc = hatj-hatk

USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

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  2. solve:e^-x(d^2y)/dx^2=x

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  3. Find the scalar and vector projections of the vector 2hati-3hatj-6hatk...

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

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

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  6. Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...

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  7. A variable plane is at a constant distance p from the origin and meets...

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  8. Give an example of a relation f such that f = f^(-1)

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  9. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

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  10. Solve the following LPP graphically Optimize Z=5x1+25x2 subject to -0....

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  11. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  12. Find the inverse of the matrix abs[[3,-2,3],[2,1,-1],[4,-3,2]]

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  13. If A=abs[[1,2,0],[1,1,0],[-1,4,0]],B=abs[[1,2,3],[1,1,-1],[4,-3,2]] 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 coordinates of the point on the curve x^2y - x + y = 0 wher...

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  16. Evaluate intln(x^2+x+2)dx

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  17. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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  18. Solve the differential equation. x(x+y)dy=(x^2+y^2)dx

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  19. If veca,vecb,vecc are three mutually perpendicular vectors of equal ma...

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  20. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

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