Home
Class 12
MATHS
If veca and vecb are two vectors of magn...

If `veca and vecb` are two vectors of magnitude 1 inclined at `120^(@)`, then find the angle between `vecb and vecb-veca`.

Text Solution

Verified by Experts

`|veca|= |vecb|=1`
Hence, vectors `veca and vecb` are adjacent sides of rhombus `OACB`
Angle between `veca and vecb` is `120^(@)`.
Also diagonals of rhombus are OC and AB. Thus,
`" "vec(OC)= veca+vecb and vec(AB)= vecb-veca`
Clearly from the figure, angle between `vecb and vecb-veca` is `30^(@)`.
`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise 1.2|7 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Subjective)|14 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos
  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

If veca and vecb are two vectors such that |veca xx vecb|= veca.vecb , then what is the angle between veca and vecb ?

Let veca and vecb are two vectors inclined at an angle of 60^(@) , If |veca|=|vecb|=2 ,the the angle between veca and veca + vecb is

if veca,vecb and vecc are mutally perpendicular vectors of equal magnitudes, then find the angle between vectors and veca+ vecb+vecc .

vecA and vecB are two vectors of equal magnitude and theta is the angle between them.The angle between vecA or vecB with their resultant is

If veca, vecb are unit vertors such that veca -vecb is also a unit vector, then the angle between veca and vecb , is

Let veca and vecb be two vectors of the same magnitude such that the angle between them is 60^(@) and veca.vecb =8. Find |veca| and |vecb| .

If veca and vecb are two vectors, such that |veca xx vecb|=2 , then find the value of [veca vecb veca xx vecb]

If veca and vecb are two vectors, such that |veca xx vecb|=2 , then find the value of [veca vecb veca xx vecb]

CENGAGE-INTRODUCTION TO VECTORS -Exercise 1.1
  1. Find the unit vector in the direction of the vector veca=hati+hatj+2ha...

    Text Solution

    |

  2. Find the direction cosines of the vector hati+2hatj+3hatk.

    Text Solution

    |

  3. Find the direction cosines of the vector joining the points A(1, 2, -3...

    Text Solution

    |

  4. The position vectors of P and Q are 5hati+4hatj+ahatk and -hati+2hatj-...

    Text Solution

    |

  5. Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find ...

    Text Solution

    |

  6. Find a vector of magnitude 5 units, and parallel to the resultant of t...

    Text Solution

    |

  7. Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are col...

    Text Solution

    |

  8. If A B C D is a rhombus whose diagonals cut at the origin O , then ...

    Text Solution

    |

  9. Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , re...

    Text Solution

    |

  10. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

    Text Solution

    |

  11. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

    Text Solution

    |

  12. If vec A O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O ...

    Text Solution

    |

  13. If the sides of an angle are given by vectors veca=hati-2hatj+2hatk an...

    Text Solution

    |

  14. A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD...

    Text Solution

    |

  15. A B C D is a quadrilateral and E and the point intersection of the ...

    Text Solution

    |

  16. What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ...

    Text Solution

    |

  17. The position vectors of points A and B w.r.t. the origin are veca=hati...

    Text Solution

    |

  18. If vec r1, vec r2, vec r3 are the position vectors off thee collinear...

    Text Solution

    |

  19. If veca and vecb are two vectors of magnitude 1 inclined at 120^(@), t...

    Text Solution

    |

  20. Find the vector of magnitude 3, bisecting the angle between the vector...

    Text Solution

    |