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Prove that (vecaxxhati)^2+(vecaxxhatj)^2...

Prove that `(vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2` .

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  2. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  3. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2 .

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  4. Find the equation of planes passing throught the points (6,-1,1), (5,1...

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  5. Find the co-ordinates of the foot of the perpendicular drawn from the ...

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  6. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  7. If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y(n+2)+(2n+1)xy(n+1)+(...

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  8. Show that the rectangle of maximum area that can be inscribed in a giv...

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  9. Prove the following by vector method. Altitudes of a triangle are conc...

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  10. Find the magnitude and equation of the line of shotest distance betwee...

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

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  12. Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(...

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  13. Show that the function f : R^+toR^+ defined by f (x) =x+1/x is injecti...

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  14. Solve "sin"^(-1)x-"cos"^(-1)x="cos"^(-1)sqrt(3)/(2)

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  15. Solve: 2sin^(-1) x +sin^(-1) (1-x)= pi/2

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

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  17. int0^pi((xtanx)/(secx+tanx))dx

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

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  19. Differentiate cos^(-1)(sinx) w.r.t.x.

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  20. int(cot xdx)/(ln sin x) = ?

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