Home
Class 12
MATHS
If veca , vecb , vecc are positi...

If `veca , vecb , vecc` are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is `1/2 ​ [ veca × vecb + vecb × vecc + vecc × veca ]`. Also deduce the condition for collinearity of the points A, B and C.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos
  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If veca , vecb, vecc are the position vectors of the vertices. A,B,C of a triangle ABC. Then the area of triangle ABC is

[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb vecc ] , then

If veca, vecb and vecc are the position vectors of the vertices A,B and C. respectively , of triangleABC . Prove that the perpendicualar distance of the vertex A from the base BC of the triangle ABC is (|vecaxxvecb+vecbxxvecc+veccxxveca|)/(|vecc-vecb|)

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then:

If veca , vecb , vecc are unit vectors such that veca+ vecb+ vecc= vec0 find the value of (veca* vecb+ vecb* vecc+ vecc*veca) .

If veca, vecb, vecc are three non-zero vectors such that veca + vecb + vecc=0 and m = veca.vecb + vecb.vecc + vecc.veca , then:

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) =

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc) is

Let ABC be a triangle whose circumcenter is at P, if the positions vectors of A,B,C and P are veca,vecb,vecc and (veca + vecb+vecc)/4 respectively, then the positions vector of the orthocenter of this triangle, is:

Let veca, vecb and vecc be unit vector such that veca + vecb - vecc =0 . If the area of triangle formed by vectors veca and vecb is A, then what is the value of 4A^(2) ?

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= ...

    Text Solution

    |

  2. If | vec a|=2, then find the value of | vec axx hat i|^2+| vec axx hat...

    Text Solution

    |

  3. If veca , vecb , vecc are position vectors of the vertices A, ...

    Text Solution

    |

  4. A , B , Ca n dD are any four points in the space, then prove that |...

    Text Solution

    |

  5. Find the area of the parallelogram whose adjacent sides are determin...

    Text Solution

    |

  6. Using vectors, find the area of the triangle with vertices A (1, 1,...

    Text Solution

    |

  7. Let vec a , vec ba n d vec c be three verctors such that vec a!=0...

    Text Solution

    |

  8. Find the area a parallelogram whose diagonals are vec a=3 hat i+ ha...

    Text Solution

    |

  9. If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 ve...

    Text Solution

    |

  10. If vec aa n d vec b are any two unit vectors, then find the greate...

    Text Solution

    |

  11. If the vectors vec a , vec b ,a n d vec c form the sidesB C ,C Aa n d...

    Text Solution

    |

  12. Let vec u be a vector on rectangular coordinate system with slopin...

    Text Solution

    |

  13. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |

  14. Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equall...

    Text Solution

    |

  15. Volume of parallelepiped formed by vectors vec axx vec b , vec bxx...

    Text Solution

    |

  16. Given three vectors vec a , vec b ,a n d vec c two of which are non-c...

    Text Solution

    |

  17. The value of a so that the volume of parallelepiped formed by hat i...

    Text Solution

    |

  18. A1,A2,..., An are the vertices of a regular plane polygon with n sides...

    Text Solution

    |

  19. If c is a given non-zero scalar, and vec A and vec(B) are given ...

    Text Solution

    |

  20. A , B , Ca n dD are any four points in the space, then prove that |...

    Text Solution

    |