Home
Class 12
MATHS
Show that the following vector are co-pl...

Show that the following vector are co-planar. `hati-2hatj+2hatk, 3hati+4hatj+5hatk, -2hati+4hatj-4hatk`.

Text Solution

Verified by Experts

Let `veca = hati-2hatj+2hatk`
`vecb = 3hati+4hatj+5hatk`
`vecc = -2hati+4hatj-4hatk`

The vectors `veca.vecb.vecc` are coplanar if `(vecaxxvecb).vecc = 0`
Hence as `(vecaxxvecb).vecc = 0 the given vectors are coplanar.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|267 Videos

Similar Questions

Explore conceptually related problems

Show that the following vector are co-planar. hati+2hatj+3hatk, -2hati-4hatj+5hatk, 3hati+6hatj+hatk

Find the value of lambda such that the following vectors are coplanar: -hati+lambdahatj -lambdahatk, 2hati+4hatj +5hatk, -2hati+4hatj -4hatk

Find the value of lambda so that the three vectors are co-planar. hati+2hatj+3hatk, 4hati+hatj+lambdahatk and lambdahati-4hatj+hatk

Prove that the vectors 2hati-hatj+hatk , hati-3hatj-5hatk , 3hati-4hatj-4hatk are the sides of a right angled triangle.

Prove that four points with position vectors hati+hatj-3hatk, 2hati -hatj-hatk,- hati +2hatj +2hatk and 2hati +2hatk arecoplanar

Find a unit vector perpendicular to the following two vectors veca =2hati+3hatj+6hatk and vecb = 3 hati-6 hatj+2 hatk

Find the scalar triple product vecb.(veccxxveca) where veca, vecb and vecc are respectively 5hati-hatj+4hatk, 2hati+3hatj+5hatk, 5hati-2hatj+6hatk

If veca = hati+2hatj-hatk , vecb = hati+hatj+2hatk , vecc = 2hati-hatj then

Show that the vectors 4hati+4hatj+ 4hatk,7hati+6hatj-hatk and 3hati+2hatj-5hatk form a right angled triangle and find its area.

The position vectors of the points A, B, C and D are 4hati+3hatj-hatk , 5hati+2hatj+2hatk , 2hati-2hatj-3hatk and 4hati-4hatj+3hatk respectively. Show that AB and CD are parallel.

MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Find the volume of the parallelopiped whose sides are given by the vec...

    Text Solution

    |

  2. Find the volume of the Parallelepiped whose sides are given by the vec...

    Text Solution

    |

  3. Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+...

    Text Solution

    |

  4. Show that the following vector are co-planar. hati+2hatj+3hatk, -2hati...

    Text Solution

    |

  5. Find the value of lambda so that the three vectors are co-planar. hati...

    Text Solution

    |

  6. Find the value of lambda so that the three vectors are co-planar. (2,-...

    Text Solution

    |

  7. If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbx...

    Text Solution

    |

  8. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

    Text Solution

    |

  9. Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

    Text Solution

    |

  10. For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk, obtain vec...

    Text Solution

    |

  11. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

    Text Solution

    |

  12. If veca, vecb, vecc be unit vectors and vecaxx(vecbxxvecc) = 1/2hatb, ...

    Text Solution

    |

  13. Prove that the sum of the vectors directed from the vertices to the mi...

    Text Solution

    |

  14. Prove by vector method that the diagonals of a quadrilateral bisect ea...

    Text Solution

    |

  15. If G is the centroid of a triangle ABC, prove that vec(GA)+vec(GB)+vec...

    Text Solution

    |

  16. If M is the midpoint of the side vec(BC) of a triangle ABC, prove that...

    Text Solution

    |

  17. If veca and vecb are unit vectors represented by the adjacent sides of...

    Text Solution

    |

  18. If the points with position vectors 10hati+3hatj, 12hati-5hatj and aha...

    Text Solution

    |

  19. Prove that the four points with position vectors 2veca+3vecb-vecc, vec...

    Text Solution

    |

  20. For any vector vecr = xhati+yhatj+zhatk, prove that vecr = (vecr.hati)...

    Text Solution

    |