Home
Class 12
MATHS
Find the value of lambda so that the thr...

Find the value of `lambda` so that the three vectors are co-planar. (2,-1,1), (1,2,-3) and (3,λ,5)

Text Solution

Verified by Experts

Let `veca = (2,-1,1), vecb = (1,2,-3), vecc = (3,lambda,5)`
If `veca,vecb,vecc` are coplanar then `vecaxxvecb.vecc = 0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|267 Videos

Similar Questions

Explore conceptually related problems

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

Find the value of a so that the points (1,4),(2,7),(3,a) are collinear.

Find the value of lambda so that three vectors veca=2hati-hatj+hatk, vecb=hati+2hatj-3 hatk and vecc= 3hati +lambda vecj+5 hatk are coplanar.

Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = (6,2,-3), vecb = (1,-4, lambda )

Find the value of lambda so that the vectors veca and vecb are perpendicular to each other. veca = 3hati+4hatj , vecb = -5hati+lambdahatj .

MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Show that the following vector are co-planar. hati+2hatj+3hatk, -2hati...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and ...

    Text Solution

    |

  19. If veca makes equal angles with hati, hatj and hatk and has magnitude ...

    Text Solution

    |

  20. If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that v...

    Text Solution

    |