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Prove (i) r = (r.i) i+(r.j)j+(r.k)k ...

Prove
(i) `r = (r.i) i+(r.j)j+(r.k)k `
(ii) `ixx(axxi) +jxx(axxj)+kxx(axxk) =2a`
(iii) `[(ixxa).b] i+[(jxxa).b] +[(kxxa).b] .k = axxb`

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ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (2) (TRUE AND FALSE)
  1. Prove by vector method, that in a right-angled triangle ABC, AB^(2) + ...

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  2. Prove using vectors: The median to the base of an isosceles triangl...

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  3. (i) If |a + b| = |a -b|, then a and b are parallel. True or False

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  4. If |a|=a and | vec b|=b , prove that ( vec a/( vec a^2)- vec b/(b^2))^...

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  5. If the vectors a, b and c are complanar, then |{:(1, b, c),(a*a, a*b,a...

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  6. Prove that |axxb|^2 =a^2b^2 - (a.b)^2

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  7. If a , b, c be the vectors determined by sides BC, CA and AB of a tria...

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  8. Prove (i) r = (r.i) i+(r.j)j+(r.k)k (ii) ixx(axxi) +jxx(axxj)+kx...

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  9. The ratio of lengths of diagonals of the parallelogram constructed on ...

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  10. A vector of magnitude 9 perpendicular to both the vectors a = 4i - j+k...

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  11. The area of a parallelogram constructed on the vectors a +3b and 3a +b...

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  12. Let a = i +2j -3k and b = 2i +j-k then the vector r satisfying a xx r ...

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  13. If a, b, c, are non-zero vectors such that a xx b = b xx c then a + c ...

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  14. If T(p), T(q) and T(r) of a G.P. are +ive numbers a, b, c respectively...

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  15. In a triangle ABC, cos 3A + Cos 2B + cos 2C ge -3//2 . True or Fals...

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  16. For any two vectors u and v, find if (1+|u|^(2))(1+|v|^(2)) = (1-u....

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  17. Using dot product of vectors; prove that a parallelogram; whose diagon...

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  18. If AC and BD are the diagonals of a quadrilateral ABCD, prove that its...

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  19. IF a quadrilateral ABCD is such that vecAB = b, vecAD = d and vecAC = ...

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  20. If a and b are non-collinear, then the point of intersectioon of the ...

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