Home
Class 12
MATHS
Find λ if the vectors vec a = hat i+3 ha...

Find `λ` if the vectors `vec a = hat i+3 hat j +hat k, vec b=2 hat i- hat j- hat k and vec c=λ hat j+3 hat k` are coplanar.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Find λ if vectors vec a = hat i +λ hat j +hat k, vec b= 2hat i -hat j-hat k and vec c =7 hat j +3hat k are coplanar.

Find λ such that the vectors vec a =hat i +3 hat j +hat k, vec b= 2 hat i -hat j - hat k and vec c= λ hat i +7 hat j +3 hat k are coplanar.

Find the value of scalar λ if the vectors vec a =2 hat i +hat j +hat k, vec b= hat i -hat j+2hat k and vec c =λ hat i +3 hat j -2 hat k are coplanar.

Prove that the vectors vec a = hat i- 2 hat j+ hat k , vec b= -2 hat i+ hat j+ hat k and vec c= hat i+ hat j-2 hat k are coplanar.

Show that the vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + 3hat j- 4hat k and vec c =hat i - 3 hat j+5 hat k are coplanar.

Show that the vectors vec a = hat i- 3 hat j+ 2 hat k , vec b= 2 hat i- 4 hat j- 4hat k and vec c= 3 hat i+ 2 hat j- 3hat k are linearly independent.

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = 2 hat i- 3 hat j + 4 hat k, vec b= hat i +2 hat j- hat k and vec c = 3 hat i -hat j +2 hat k .

Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat i- hat j+ hat k and vec c= hat i+ 2 hat j+ 6 hat k from of a right angled triangle.

Find λ such that the vectors vec v_1 =2 hat i - hat j +hat k, vec v_2= hat i +2hat j -3 hat k and vec v_3= 3 hat i +λ hat j +5 hat k are coplanar.

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = -3hat i+7 hat j + 5 hat k, vec b=-5 hat i +7 hat j- 3 hat k and vec c = 7 hat i -5 hat j -3 hat k .

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Prove that the points whose position vectors are 6 hat i - 7 hat j, 16...

    Text Solution

    |

  2. Find x such that the four points A (4, 1, 2), B (5, x, 6), C (5, 1,-1)...

    Text Solution

    |

  3. Find λ if the vectors vec a = hat i+3 hat j +hat k, vec b=2 hat i- hat...

    Text Solution

    |

  4. Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b...

    Text Solution

    |

  5. For any three vectors vec a,vec b and vec c , show that vec a- vec b,v...

    Text Solution

    |

  6. Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

    Text Solution

    |

  7. Integrate the following int (cosx)dx/(1+sin^2x)

    Text Solution

    |

  8. Prove that if vec a,vec b,vec c and vec d are any four vectors, then (...

    Text Solution

    |

  9. Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, ve...

    Text Solution

    |

  10. Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, ve...

    Text Solution

    |

  11. Find the volume of the Parallelopiped whose coterminous edges are repr...

    Text Solution

    |

  12. Find the volume of the Parallelopiped whose coterminous edges are repr...

    Text Solution

    |

  13. Find the volume of the Parallelopiped whose coterminous edges are repr...

    Text Solution

    |

  14. If vec α and vec β are any vectors, prove that vec β * (vec α xx vec β...

    Text Solution

    |

  15. If vec a = -2hat i -2 hat j + 4 hat k, vec b=-2 hat i +4 hat j- 2 hat...

    Text Solution

    |

  16. Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 ha...

    Text Solution

    |

  17. If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and ...

    Text Solution

    |

  18. Integrate the following int xe^(3x)dx

    Text Solution

    |

  19. Find λ if vectors vec a = hat i +λ hat j +hat k, vec b= 2hat i -hat ...

    Text Solution

    |

  20. Find the value of scalar λ if the vectors vec a =2 hat i +hat j +hat ...

    Text Solution

    |