Home
Class 12
MATHS
Show that each of the given three vector...

Show that each of the given three vectors is a unit vector : `1/7 (2 hat i +3 hat j + 6 hat k), 1/7 (3hat i -6 hat j + 2 hat k), 1/7 (6 hat i +2 hat j -3 hat k)` Also, show that they are mutually perpendicular to each other.

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 the unit vector in the direction of sum of vectors -2 hat i- 3 hat j+ 2 hat k , 3 hat i+ 4 hat j- 2 hat k and hat i+ 2 hat j+ 6 hat k .

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 7 hat i+ hat j- 3 hat k .

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 2 hat i+ 6 hat j+ 3 hat k .

Calculate the product ((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j- 3 hat k)) * (-3 hat i+ hat j+ 2 hat k ) .

Prove that the vectors 2 hat i- hat j+ hat k , hat i- 3 hat j- 5 hat k and 3 hat i- 4 hat j- 4 hat k are coplanar.

Show hat the vectors vec a=1/7 (2 hat i+3 hat j+6 hat k) , vec b=1/7(6 hat i+2 hat j-3 hat k) and vec c=1/7(3 hat i-6 hat j+2 hat k) are mutually orthogonal unit vectors.

Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and hat i+ λ hat j- 3 hat k are coplanar.

Find a unit vector perpendicular to both the vectors (3 hat i + 2 hat j - hat k) and ( hat i + 2 hat j + hat k) .

Show that the vectors 2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j -8 hat k are collinear.

Prove that the points whose position vectors are hat i - hat j+ hat k , 2 hat i+ 3 hat j+ hat k , hat i+ 2 hat j+ 3 hat k , -2 hat j+ 3 hat k lie in the same plane.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the projection of the vector hat i - hat j on the vector hat i +...

    Text Solution

    |

  2. Find the projection of the vector hat i +3 hat j +7 hatk on the vector...

    Text Solution

    |

  3. Show that each of the given three vectors is a unit vector : 1/7 (2 ha...

    Text Solution

    |

  4. Find |vec a| and |vec b| lf(veca + vec b)*(vec a-vec b)=8 and |vec a |...

    Text Solution

    |

  5. Evaluate the product (3 vec a-5 vec b)*(2 vec a+7 vec b).

    Text Solution

    |

  6. Find the magnitude of two vectors veca and vecb, having the same magni...

    Text Solution

    |

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

    Text Solution

    |

  8. Show that |vec a|vec b + |vec b|vec a perpendicular to |vec a|vec b - ...

    Text Solution

    |

  9. If |a|=5,|a-b|=8 and |a+b|=10, then |b| is equal to

    Text Solution

    |

  10. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

    Text Solution

    |

  11. If either vector veca = 0or vecb = 0, then veca cdot vecb = 0.But the...

    Text Solution

    |

  12. If the vertices A, B, C of a triangle ABC are (1,2,3), (-1,0,0), (0,1,...

    Text Solution

    |

  13. Show that the points A(1,2,7), B(2,6,3) and C(3,10,-1) are collinear.

    Text Solution

    |

  14. Show that the points A(2 hat i - hat j + hat k), B(hat i - 3 hat j- 5 ...

    Text Solution

    |

  15. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

    Text Solution

    |

  16. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

    Text Solution

    |

  17. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

    Text Solution

    |

  18. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

    Text Solution

    |

  19. Find |vec a xx vec b|, if vec a = 2hat i-5 hat j+3 hat k and vec b = h...

    Text Solution

    |

  20. Find a unit vector perpendicular to each of the vectors vec a+vec b an...

    Text Solution

    |