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If tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)...

If `tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)/(yr)]+ tan^(-1) [(xy)/(zr)] = pi /2` prove that, `x^2 + y^2 + z^2 = r^2`.

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UNITED BOOK HOUSE-SET 15-EXERCISE
  1. If P(A) = 2P(B) = 2/5 and P(B/A) = 1/3, find P(A/B) and P(AuuB).

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  2. A pair of dice is thrown 3 times. Find the probability of getting a do...

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  3. If tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)/(yr)]+ tan^(-1) [(xy)/(zr)] =...

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  4. If A = [[1,-1],[2,-1]],B = [[a,1],[b,-1]] and (A+B)^2 = A^2+B^2 find a...

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  5. Prove that, [[1+x,1,1],[1,1+y,1],[1,1,1+z]] = xyz(1 + 1/x+1/y+1/z)

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  6. Solve :[[x-2,2x-3,3x-4],[x-4,2x-9,3x-16],[x-8,2x-27,3x-64]]=0

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  7. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  8. Evaluate:int e^(4x)sin 3x dx

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  9. Evaluate:int (tan theta d theta)/(1-sin theta)

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  10. Solve:(x+y+1)dx + (2x+2y-1)dy = 0

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  11. solve:(dy)/(dx) + (sin 2y)/(x) = x^3cos^2y.

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  12. If the vectors a hati + hatj + hatk, hati + b hatj + hatk and hati + h...

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  13. If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx ...

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  14. Evaluate (with the help of definite integral): underset(n rarr infty)l...

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  15. find the value of underset(2)overset(3)int a^x dx(a<0).

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  16. Two cards are drawn successively with replacement from a well-shuffled...

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  17. Find the maximum value of f(x)=(1/x)^x

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  18. Solve: xdx+ ydy+ (xdy-ydx)/(x^2+y^2)=0 given y = 1 when x= 1.

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  19. Find the equation of the plane which contains the two parallel line: (...

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  20. A and B are two independent events such that P(AuuB) = 0.8 and P(A) = ...

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