Home
Class 11
PHYSICS
The sum and difference of two vectors ve...

The sum and difference of two vectors `vec(A)` and `vec(B)` are `vec(A) +vec(B) = 2hati +6 hatj + hatk` and `vec(A) - vec(B) = 4 hati +2 hatj - 11 hatk`. Find the magnitude of each vector and their scalar product `vec(A) vec(B)`.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(50),sqrt(41),-25`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

The sum and difference of two vectors vec A and vec B are , vec A+vec B=2hat i+6hat j+hat k and vec A-vec B=4hat i+2hat j-11hat k . Find the magnitude of each vector and their scalar product vec A.vec B .

If vec(A) = 3 hati +2hatj and vec(B) = hati - 2hatj +3hatk , find the magnitudes of vec(A) +vec(B) and vec(A) - vec(B) .

Find the angle between the vectors vec(A) = 2 hati - 4hatj +6 hatk and vec(B) = 3 hati + hatj +2hatk .

Prove that the vectors vec(A) = 2hati - 3hatj - hatk and vec(B) =- 6 hati + 9hatj +3hatk are parallel.

If vec(A) = hati + 3hatj + 2hatk and vec(B) = 3hati + hatj + 2hatk , then find the vector product vec(A) xx vec(B) .

If vec(A) and vec(B) are two such vectors that |vec(A)| = 2, |vec(B)| = 7 and vec(A) xx vec(B) = 3 hati +2 hatj + 6 hatk , find the angle between vec(A) and vec(B) .

If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk , then find the value of (vec(A) +vec(B)) xx (vec(A) - vec(B))

Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3 hatk and vec(B) =- 2hati + hatj - 2hatk .

What is the projection of vec(A) = hati + hatj+ hatk on vec(B) = (hati + hatk)

Find the angle between the vertors vec(A) = hati + 2hatj - hatk and vec(B) = - hati +hatj - 2hatk .

SL ARORA-VECTORS-Problems For Self Practice
  1. A force vec(F) = 4 hati + hatj + 3hatk newton acts on a particle and d...

    Text Solution

    |

  2. Under a force of 10 hati - 3 hatj +6 hatk newton, a body of mass 5 kg ...

    Text Solution

    |

  3. The sum and difference of two vectors vec(A) and vec(B) are vec(A) +ve...

    Text Solution

    |

  4. A force vec(F) = 5hati + 4hatj newton displaces a body through vec(S) ...

    Text Solution

    |

  5. If the resultant of the vectors 3 hati +4 hatj +5 hatk and 5 hati +3 h...

    Text Solution

    |

  6. Show that the vectors a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk and ...

    Text Solution

    |

  7. If vectors vec(A),vec(B) and vec(C) have magnitudes 8,15 and 17 units ...

    Text Solution

    |

  8. If vec A =vec B- vec C, then determine the angle between vec A and ve...

    Text Solution

    |

  9. For two vectors vec(A) and vec(B) if vec(A) + vec(B) = vec(C) and A +B...

    Text Solution

    |

  10. Prove that (vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos the...

    Text Solution

    |

  11. Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 ha...

    Text Solution

    |

  12. If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk, th...

    Text Solution

    |

  13. Find the value of a for which the vectors 3 hati + 3hatj + 9 hatk and ...

    Text Solution

    |

  14. Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3...

    Text Solution

    |

  15. Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj...

    Text Solution

    |

  16. Find a vector of magnitude 18 which is perpendicular to both the vecto...

    Text Solution

    |

  17. Determine the area of the parallelogram whose adjacent sides are forme...

    Text Solution

    |

  18. Find the area of the triangle formed by points O,A and B such that vec...

    Text Solution

    |

  19. Find with the help of vectors, the area of the triangle with vertices ...

    Text Solution

    |

  20. If vec(A) and vec(B) are two such vectors that |vec(A)| = 2, |vec(B)| ...

    Text Solution

    |