Home
Class 12
MATHS
If |a|=a and | vec b|=b , prove that ( v...

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

Text Solution

Verified by Experts

The correct Answer is:
T
Promotional Banner

Topper's Solved these Questions

  • ADDITION AND MULTIPLICATION OF VECTORS

    ML KHANNA|Exercise Problem Set (2) (FILL IN THE BLANKS) |23 Videos

  • ADDITION AND MULTIPLICATION OF VECTORS

    ML KHANNA|Exercise Problem Set (3) (MULTIPLE CHOICE QUESTIONS) |104 Videos

  • ADDITION AND MULTIPLICATION OF VECTORS

    ML KHANNA|Exercise Problem Set (2) (MULTIPLE CHOICE QUESTIONS) |165 Videos

  • AREA OF CURVES

    ML KHANNA|Exercise SELF ASSESSEMENT TEST|16 Videos

Similar Questions

Explore conceptually related problems

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

If |vec a|=a and |vec b|=b then prove that ((vec a)/(a^(2))-(vec b)/(b^(2)))=((vec a-vec b)/(ab))^(2)

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

For any two vectors vec a and vec b, prove that ((vec a) / (| vec a | ^ (2)) - (vec b) / (| vec b | ^ (2))) ^ (2) = ((vec a-vec b) / (| vec a || vec b |)) ^ (2)

Prove that (vec(a)-vec(b)) xx (vec(a) +vec(b))=2(vec(a) xx vec(b))

Prove that (vec(a) + vec(b)) xx (vec(a) - vec(b)) = 2 (vec(b) xx vec(a))

Prove that (vec a * vec b) ^ (2) <= vec a ^ (2) * vec b ^ (2)

Prove that |vec a + vec b| = sqrt (|vec a|^2 + |vec b|^2 + 2 vec a * vec b) .

If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a - vec b) * (3 vec a + vec b) .

For any two vectors vec a and vec b ,prove that (vec a xxvec b)^(2)=|vec a|^(2)|vec b|^(2)-(vec a*vec b)^(2)

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) + ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |