Home
Class 12
MATHS
Prove that : |veca + vecb|le|veca|+|vecb...

Prove that : `|veca + vecb|le|veca|+|vecb|`.

Text Solution

Verified by Experts


Let ABC be the triangle where `vec(AB) = veca. vec(BC) = vecb`
Then `vec(AC) = veca=vecb`
Now `|veca| = AB, |vecb| = BC` and `|veca+vecb| = AC`
In the triangle ABC,
`AC `implies |veca+vecb|<|veca|+|vecb|`
Now AC = AB+BC when A,B,C lie on a straight line A,B,C are collinear.
Hence `|veca+vecb| = |veca|+|vecb|`
When `veca` and `vecb` are like collinear vectors or zero vectors.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|267 Videos

Similar Questions

Explore conceptually related problems

|veca| = |vecb| = veca = vecb .

Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (veca xx vecb) = vec0 and hence prove that veca xx (vecb xx vecc), vecb xx (vecc xx veca), vecc xx (veca xx vecb) are coplanar.

State when the equality will hold, |veca - vecb|ge|veca|-|vecb|

If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and veca.vecb = 6, find |veca+vecb| and |veca-vecb| .

Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)

Vectors veca,vecb, vecc are such that veca + vecb + vecc = 0 and |veca| = 3, |vecb| = 5 and |vecc]= 7 . Find the angle between veca and vecb .

What is geometrical significance of the relation |veca+vecb| = |veca-vecb|

If veca,vecb and vecc are three vectors such that veca x vecb = vecc and vecb x vecc = veca , then prove that veca,vecb and vecc are mutually at right angles and |vecb| = 1,|vecc| = |veca|

For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Prove that the sum of all the vectors drawn from the centre of a regul...

    Text Solution

    |

  2. Prove that the sum of the vectors represented by the sides of a closed...

    Text Solution

    |

  3. Prove that : |veca + vecb|le|veca|+|vecb|.

    Text Solution

    |

  4. State when the equality will hold, |veca - vecb|ge|veca|-|vecb|

    Text Solution

    |

  5. What is geometrical significance of the relation |veca+vecb| = |veca-v...

    Text Solution

    |

  6. Find the magnitude of the vector vec(PQ), its scalar components and th...

    Text Solution

    |

  7. Find the magnitude of the vector vec(PQ), its scalar components and th...

    Text Solution

    |

  8. Find the magnitude of the vector vec(PQ), its scalar components and th...

    Text Solution

    |

  9. In each of the following find the vector vec(PQ), its magnitude and di...

    Text Solution

    |

  10. In each of the following find the vector vec(PQ), its magnitude and di...

    Text Solution

    |

  11. If veca = (2,-2,1), vecb = (2,3,6) and vecc = (-1,0,2), Find the magni...

    Text Solution

    |

  12. Determine the unit vector having the direction of the given vector in ...

    Text Solution

    |

  13. Determine the unit vector having the direction of the given vector in ...

    Text Solution

    |

  14. Determine the unit vector having the direction of the given vector in ...

    Text Solution

    |

  15. Determine the unit vector having the direction of the given vector in ...

    Text Solution

    |

  16. Find the unit vector in the direction of the vector vecr1-vecr2, where...

    Text Solution

    |

  17. Find the unit vector parallel to the sum of the vectors veca = 2hati+4...

    Text Solution

    |

  18. If the sum of the two unit vectors, show that the magnitude of their d...

    Text Solution

    |

  19. The position vectors of the points A, B, C and D are 4hati+3hatj-hatk,...

    Text Solution

    |

  20. In each of the following problems, show by vector method that the give...

    Text Solution

    |