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

If `a ,b ,c` are the lengths of sides, `B C ,C A` and `A B` of a triangle `A B C ,` prove that ` vec B C+ vec C A+ vec A B= vec O` and deduce that `a/(sinA)=b/(sinB)=c/(sinC)dot`

Promotional Banner

Topper's Solved these Questions

  • THE PLANE

    RD SHARMA ENGLISH|Exercise All Questions|305 Videos

Similar Questions

Explore conceptually related problems

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

If G is the centroid of a triangle A B C , prove that vec G A+ vec G B+ vec G C= vec0dot

If G is the centroid of a triangle A B C , prove that vec G A+ vec G B+ vec G C= vec0dot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If veca , vec b and vec c represents three sides of a triangle taken in order prove that veca xx vec b = vec b xx vec c = vec c xx vec a

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

A B C D E is pentagon, prove that vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

Prove that: ( vec a- vec b)*{( vec b- vec c)xx(vec c- vec a)}"=0

RD SHARMA ENGLISH-VECTOR OR CROSS PRODUCT -All Questions
  1. Find the area of the triangle formed by O ,A ,B when vec O A= hat ...

    Text Solution

    |

  2. If vec a= hat i-2 hat j+3 hat k , and vec b=2 hat i+3 hat j-5 hat k ...

    Text Solution

    |

  3. If a ,b ,c are the lengths of sides, B C ,C A and A B of a trian...

    Text Solution

    |

  4. (22) if vec p and vec qare unit vectors forming an angle of 30^@; find...

    Text Solution

    |

  5. If vec p and vec q are unit vectors forming an angle of 30^0; ...

    Text Solution

    |

  6. Find a unit vector perpendicular to each of the vectors vec(a) + vec(b...

    Text Solution

    |

  7. Find the area of the parallelogram whose diagonals are : 4 hat i- ...

    Text Solution

    |

  8. Find Find the area of the parallelogram determined by the vectors: 2 ...

    Text Solution

    |

  9. Find a vector of magnitude 49, which is perpendicular to both the v...

    Text Solution

    |

  10. If vec a=3 hat i- hat j-2 hat k and vec b=2 hat i+3 hat j+ hat k , ...

    Text Solution

    |

  11. If vec a=3 hat i-2 hat k and vec b=- hat i+3 hat k , find | veca x...

    Text Solution

    |

  12. Using vectors: Prove that if a,b,care the lengths of three sides of a ...

    Text Solution

    |

  13. Prove by vector method that the parallelogram on the same base and ...

    Text Solution

    |

  14. If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respective...

    Text Solution

    |

  15. Let vec O A= vec a , vec O B=10 vec a+2 vec b ,a n d vec O C=bw h e r...

    Text Solution

    |

  16. A B C D is quadrilateral such that vec A B= vec b , vec A D= vec d , ...

    Text Solution

    |

  17. If veca , vec b , vec c are three vectors such that veca+ vec b+ vec...

    Text Solution

    |

  18. Prove that the normal to the plane containing three points whose po...

    Text Solution

    |

  19. If vec axx vec b= vec axx vec c , vec a!= vec0a n d vec b!= vec c , s...

    Text Solution

    |

  20. For any two vectors vec aa n d vec b , show that (1+| vec a|^2)(1+| v...

    Text Solution

    |