Home
Class 12
MATHS
The length of the longer diagonal of the...

The length of the longer diagonal of the parallelogram constructed on `5 vec a+2 vec b\ a n d\ vec a-3 vec b\ ` if it is given that `| vec a|=2sqrt(2),\ | vec b|=3` and angle between ` vec a\ a n d\ vec b\ i s` `pi//4` is a.`15` b. `sqrt(113)` c. `sqrt(593)` d. `sqrt(369)`

Text Solution

Verified by Experts

Length of the two diagonals will be
`Rightarrow d_1 = |(5a + 2b) + (a-3b)|`
`Rightarrow d_2 = |(5a+2b)-(a-3b)|`
`Rightarrow d_1 = |6a-b|` and `Rightarrow d_2 = |4a+5b|`
...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|197 Videos

  • SCALAR TRIPLE PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|59 Videos

Similar Questions

Explore conceptually related problems

The lengths of the diagonals of a parallelogram constructed on the vectors vec p=2vec a+vec b and vec q=vec a-2vec b where vec a&vec b are unit vectors forming an angle of 60^(@) are:

I|vec a|=sqrt(3)|vec b|=2 and vec a*vec b=sqrt(3), find the angle between vec a and vec b

If | vec a|=sqrt(26), | vec b|=7 a n d | vec axx vec b|=35 , fin d vec adot vec bdot

Q.2 The lengths of the diagonals of a parallelogram constructed on the vectors vec p=2vec a+vec b&vec q=vec a-2vec b .where vec a&vec b are unit vectors forming an angle of 60^(@) are

If vec a+2"" vec b+3"" vec c="" vec0 and |"" vec a|=6,|"" vec b|=3a n d|"" vec c|=2 , then angle between vec aa n d"" vec b is

If vec(a) and vec(b) are vectors such that |vec(a)|=sqrt(3), |vec(b)|=2 and vec(a).vec(b)=sqrt(6) then the angle between vec(a) and vec(b) is

Vectors vec a\ a n d\ vec b are such that | vec a|=3,\ | vec b|=2/3a n d\ ( vec axx vec b) is a unit vector. Write the angle between vec a\ a n d\ vec bdot

If vec(a) and vec(B) are two vectors such that |vec(a)|=|vec(b)|=sqrt(2) and vec(a).vec(b)=-1 , find the angle between vec(a) and vec(b) .

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is (pi)/(2), then

If vec a,vec b are two unit vectors such that |vec a+vec b|=2sqrt(3) ,then the angle b

RD SHARMA-SCALAR OR DOT PRODUCT-Solved Examples And Exercises
  1. If vec a\ a n d\ vec b are unit vectors, then which of the following...

    Text Solution

    |

  2. If the vectors hat i-2x hat j+3y hat k\ a n d\ hat i+2x hat j-3y hat...

    Text Solution

    |

  3. The vector component of vec b perpendicular to vec a is ( vec bdot v...

    Text Solution

    |

  4. The length of the longer diagonal of the parallelogram constructed o...

    Text Solution

    |

  5. If vec a is a non zero vector a magnitude ' a^(prime)\ a n d\ lambda ...

    Text Solution

    |

  6. If theta is the angle between two vectors vec a\ a n d\ vec b ,\ t h...

    Text Solution

    |

  7. The values of x for which the angle between vec a=2x^2\ hat i+4x hat...

    Text Solution

    |

  8. If vec a ,\ vec b ,\ vec c are any time mutually perpendicular vect...

    Text Solution

    |

  9. If the vectors 3 hat i+lambda hat j+ hat k\ a n d\ 2 hat i- hat j+8 ha...

    Text Solution

    |

  10. The projection of the vector hat i+ hat j+ hat k along the vector ...

    Text Solution

    |

  11. The vectors 2 hat i+3 hat j-4 hat k\ a n d\ a hat i=b hat j+c hat k ar...

    Text Solution

    |

  12. If | vec a|=| vec b|,\ t h e n\ ( vec a+ vec b)dot( vec a- vec b)= a....

    Text Solution

    |

  13. If vec a\ a n d\ vec b are unit vectos inclined at an angle theta th...

    Text Solution

    |

  14. If vec a\ a n d\ vec b are unit vectorts, then the greatest value fo...

    Text Solution

    |

  15. If the angle between the vectors x hat i+3 hat j-7 hat k\ a n d\ x hat...

    Text Solution

    |

  16. If \ vec a\ a n d\ vec b are two unit vectors inclined at an angle t...

    Text Solution

    |

  17. Let vec a ,\ vec b ,\ vec c be three unit vectors such that | vec a...

    Text Solution

    |

  18. The orthogonal projection of vec a\ on\ vec b is (( vec adot vec b) ...

    Text Solution

    |

  19. If theta is an acute angle and the vector (sintheta) hat i+(costheta)...

    Text Solution

    |

  20. If vec a\ a n d\ vec b be two unit vectors and theta is the angle be...

    Text Solution

    |