Home
Class 12
MATHS
If a,b,c are the lengths of the sides [B...

If a,b,c are the lengths of the sides [BC],[CA] and [AB] of triangle ABC, prove that `vec BC+ vec CA + vec AB= vec 0 ` and deduce that `frac {a}{sin A}=frac {b}{sin B}=frac {c}{sin C}`.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

If ABC is triangle and D is the mid-point of [BC], prove that vec AB + vec AC= 2 vec AD .

In any triangle ABC, prove that : cos frac (A+B)(2)= sin frac (C)(2) .

In any triangle ABC, prove that : a (cos B + cos C) = 2 (b +c) sin^2 frac (A)(2) .

D,E,F are the middle points of the sides [BC],[CA],[AB] respectively of a triangle ABC. Show that : the sum of the vectors vec(AD),vec(BE),vec(CF) is zero.

In any triangle ABC, prove that : a sin (A/2+B)= (b +c) sin frac (A)(2) .

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

In any triangle ABC, prove that cos A= frac{b^2+c^2-a^2}{2bc} .

In any triangle ABC, prove that : sin frac (A-B)(2)= (a-b)/c cos frac (C)(2) .

In any triangle ABC, prove that : cos frac (B-C)(2)= 2 sin frac (A)(2) , when b+c=2a .

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If a,b,c are the lengths of the sides [BC],[CA] and [AB] of triangle A...

    Text Solution

    |

  2. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  3. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  4. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  5. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  6. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  7. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  8. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  9. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  10. Classify the following physical quantities into scalars and vectors: ...

    Text Solution

    |

  11. Find lambda in R such that |quad lambda vec a|=1, vec a being a non-ze...

    Text Solution

    |

  12. If |quad vec a|=2, find |quad 4 vec a |, |10 vec a| and |(-5 ) vec a |...

    Text Solution

    |

  13. Is it possible that |quad vec a+ vec b|= |quad vec a|+ |quad vec b|? I...

    Text Solution

    |

  14. If vec a = vec b, is it true that |quad vec a|=|quad vec b| ?

    Text Solution

    |

  15. Does |quad vec a|= |quad vec b| imply vec a= vec b?

    Text Solution

    |

  16. If A,B,C,D are the points with position vectors vec a,vec b, 3 vec a+ ...

    Text Solution

    |

  17. If vec c= 3 vec a + 4 vec b and 2 vec c = vec a- 3 vec b, show that ve...

    Text Solution

    |

  18. If the position vector of a point A is vec a + 2 vec b and vec a divi...

    Text Solution

    |

  19. If ABC is triangle and D is the mid-point of [BC], prove that vec AB +...

    Text Solution

    |

  20. If vec a = hat i + hat j+ 2hat k and vec b =2 hat i+ hat j - 2 hat k, ...

    Text Solution

    |

  21. If vec a = 5hat i - hat j- 2hat k and vec b =5 hat i+ hat j - 2 hat k,...

    Text Solution

    |