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For any two vectors veca and vec b show ...

For any two vectors `veca` and `vec b` show that `|vec a.vec b|le |vec a|.|vecb|`

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UNITED BOOK HOUSE-SET 4-EXERCISE
  1. Find the value of c that occurs in the conclusion of lagrange's MVT in...

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

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  3. For any two vectors veca and vec b show that |vec a.vec b|le |vec a|.|...

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  4. Show that the condition for the lines x= a1z+b1,y = c1z+d1 and x = a2z...

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  5. Can the two events A and B be mutually exclusive if P(A) = 1/8,P(A//B)...

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  6. Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in ...

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  7. Solve: sin^-1x+sin^-1(1-x)=cos^-1x

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  8. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

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  9. Prove that |[x,a,b],[a,x,b],[a,b,x]|=(x-a)(x-b)(x+a+b)

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  10. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  11. If y = sin^(-1){(5x+12sqrt(1-x^2))/13} then show that (dy)/(dx) = 1/sq...

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  12. If (sqrt(1-x^2))y= sin^(-1)x then show that (1-x^2)y2-3xy1-y =0

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  13. Evaluate: int(sin^(-1)x)/(1-x^2)^(3//2)dx

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  14. Evaluate: int (dx)/sqrt(2/3x^3-x^2+1/3)

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  15. Solve: x(dy)/(dx)+3y = x^2

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  16. Solve: (x^2+y^2)dy-xydx=0

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  17. If 2vec a+ 3vecb + vec c = vec 0, then show that vec axxvec b+vec bxxv...

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  18. If vec a = -hat i+hat j+2 hat k, vec b= 2 hati- hatj- hat k, and vec c...

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  19. Prove that overset(0)underset(-5) int {|x|+|x+2|+|x+5|}dx = 63/2

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  20. Prove that underset( n rarr infty) lim[1/n+sqrt(n^2-1^2)/n^2+sqrt(n^...

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