Home
Class 12
MATHS
For mutually perpendicular unit vectors ...

For mutually perpendicular unit vectors `hat(i), hat(j), hat(k)`, we have :

A

`hat(i). hat(i)=hat(j).hat(j)=hat(k).hat(k)=3`

B

`hat(i).hat(i)=hat(j).hat(j)=hat(k).hat(k)=1`

C

`hat(i).hat(i)=hat(j).hat(j)=hat(k).hat(k)=-1`

D

`hat(i).hat(i)=hat(j).hat(j)=hat(k).hat(k)=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Objective Type Questions (B. Fill in the Blanks)|17 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Objective Type Questions (C. True/False Questions)|10 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (j) Long Answer Type Questions (II)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

If with reference to a right handed system of mutually perpendicular unit vectors hat i,hat j,hat k we have vec alpha=3hat i-hat j, and vec beta=2hat i+hat j-3hat k Express vec beta in the form vec beta=vec beta_(1)+vec beta_(2), where vec beta_(1) is parallel to vec alpha and vec beta_(2) is perpendicular to vec alpha .

If with reference to the right handed system of mutually perpendicular unit vectors hat i , hat j and hat k , ->alpha=3 hat i- hat j , ->beta=2 hat i+ hat j-3 hat k , then express ->beta in the from ->beta= ->beta_1+ ->beta_2 , where -

If hat(i), hat(j), hat(k) are the unit vectors and mutually perpendicular, then [[hat(i), hat(j), hat(k)]] =

If hat(i), hat(j), hat(k) are the unit vectors and mutually perpendicular, then [[hat(i)+hat(j), hat(j)+hat(k), hat(k)+hat(i)]] =

If hat(i), hat(j), hat(k) are the unit vectors and mutually perpendicular, then [[hat(i)-hat(j), hat(j)-hat(k), hat(k)-hat(i)]] =

A vector perpendicular to hat(i)+hat(j)+hat(k) is

A unit vector perpendicular to each of the vectors 2hat(i) - hat(j) + hat(k ) and 3hat(i) - 4hat(i) - hat(k) is

Find a vector perpendicular to vector vec(A)=(hat(i)+2hat(j)-3hat(k)) as well as vec(B)=(hat(i)+hat(j)-hat(k))

What is the unit vector perpendicular to the following vectors 2 hat(i) + 2 hat(j) - hat(k) and 6 hat(i) - 3 hat(j) + 2 hat(k)

Find a unit vector perpendicular to the vectors hat(j) + 2 hat(k) & hat(i) + hat(j)

MODERN PUBLICATION-VECTOR ALGEBRA -Objective Type Questions (A. Multiple Choice Questions)
  1. If vec(a)=2hat(i)+3hat(j)-hat(k), then |vec(a)| is :

    Text Solution

    |

  2. Write the value of hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+ha...

    Text Solution

    |

  3. For mutually perpendicular unit vectors hat(i), hat(j), hat(k), we hav...

    Text Solution

    |

  4. Direction - ratios of vector vec(a)=hat(i)+hat(j)-2hat(k) are :

    Text Solution

    |

  5. If vec(a)=hat(i)+2hat(j), then |vec(a)| is :

    Text Solution

    |

  6. Direction - cosines of vec(a)=hat(i)+hat(j)-2hat(k) are :

    Text Solution

    |

  7. If p hat(i)+3hat(j) is a vector of magnitude 5, then the value of p is...

    Text Solution

    |

  8. If is the angle between any two vectors vec a and vec b , t...

    Text Solution

    |

  9. The inequality |vec(a).vec(b)|le |vec(a)||vec(b)| is called :

    Text Solution

    |

  10. The vectors vec(a) and vec(b) are perpendicular if :

    Text Solution

    |

  11. Find the angle between two vectors vec a and vec b with magnitudes 1 a...

    Text Solution

    |

  12. Find | vec a- vec b|,\ if:| vec a|=2,\ | vec b|=3\ a n d\ vec adot ve...

    Text Solution

    |

  13. The angle between the vectors : vec(a)=hat(i)+2hat(j)-3hat(k) and 3...

    Text Solution

    |

  14. The D.C.'s of the vector hat(i)+2hat(j)+3hat(k) are :

    Text Solution

    |

  15. If vec(a)=2hat(i)+2hat(j)+3hat(k), then its magnitude is :

    Text Solution

    |

  16. If vec(a) and vec(b) are unlike vectors, then the angle between them i...

    Text Solution

    |

  17. The angle between the vectors hat(i)-hat(j) and hat(j)+hat(k) is :

    Text Solution

    |

  18. If vec(a).vec(b)=|vec(a)xx vec(b)|, then angle between vector vec(a) a...

    Text Solution

    |

  19. Find the projection of the vector hat i+3 hat j+7 hat k on the vecto...

    Text Solution

    |

  20. If the angle between two vectors vec(a) and vec(b) is zero, then :

    Text Solution

    |