Home
Class 12
MATHS
Find the sum of the vectors veca=hati-2...

Find the sum of the vectors `veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5hatkandvecc=hati-6hatj--7hatk`.

Text Solution

Verified by Experts

`h=("volume of parallelepiped")/("Area of base")`
`=([vec(A)vec(B)vec(C)])/(|vec(A)xxvec(B)|)=(|(1,1,1),(2,4,-1),(1,1,3)|)/(|(hat(i),hat(j),hat(k)),(1,1,1),(2,4,-1)|)=(4)/(|-5hat(i)+3hat(j)+2hat(k)|)=(2sqrt(38))/(19)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos
  • DETERMINANTS

    CENGAGE|Exercise All Questions|268 Videos
  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

Similar Questions

Explore conceptually related problems

Show that the vectors veca=2hati+3hatj+6hatk,vecb=6hati+2hatj-3hatk, " ""and"" "vecc=3hati-6hatj+2hatk , are mutually orthogonal.

Find the altitude of a parallelepiped whose three coterminous edges are vectors vecA=hati+hatj+hatk,vecB=2hati+4hatj-hatkand vecC=hati+hatj+3hatk "with" vecA and vecB as the sides of the base of the parallelepiped .

If vectors veca =hati +2hatj -hatk, vecb = 2hati -hatj +hatk and vecc = lamdahati +hatj +2hatk are coplanar, then find the value of (lamda -4) .

Find the unit vector parallel to 3veca-2vecb+4vecc,"if"" "veca=3hati-hatj-4hatk,vecb=-2hati+4hatj-3hatk,vecc=hati+2hatj-hatk .

Find veca.vecb when veca=hati-2hatj+hatk" ""and"" " vecb=3hati-4hatj-2hatk

If veca=3hati-2hatj+hatk and vecb=2hati-4hatj+hatk then find |veca-2vecb|.

Find the resultant of vectors veca=hati-hatj+2hatk and vecb=hati+2hatj-4hatk . Find the unit vector in the direction of the resultant vector.

Find the unit vector in the direction of the sum of vectors , veca=2hati+2hatj-5hatkandvecb=2hati+hatj+3hatk .

Find the projection of the vector veca=2hati+3hatj+2k on the vector vecb=hati+2hatj+hatk .

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. Find the sum of the vectors veca=hati-2hatj+hatk,vecb=-2hati+4hatj+5h...

    Text Solution

    |

  2. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

    Text Solution

    |

  3. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|...

    Text Solution

    |

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

    Text Solution

    |

  5. If |a|=3,|b|=4a n d the angle between aa n db is 120^0 , then find the...

    Text Solution

    |

  6. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

    Text Solution

    |

  7. Let veca vecb and vecc be pairwise mutually perpendicular vectors, suc...

    Text Solution

    |

  8. If veca+vecb+vecc =0, |veca|=3, |vecb|=5, |vecc|=7 then the angle betw...

    Text Solution

    |

  9. If the angle between unit vectors veca and vecb is 60^(@) . Then find ...

    Text Solution

    |

  10. Let vecu=hai+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn is...

    Text Solution

    |

  11. A , B , C , D are any four points, prove that vec A B dot vec C D+ ...

    Text Solution

    |

  12. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1), then find the projection...

    Text Solution

    |

  13. If the vectors 3 vec p+ vec q ;5p-3 vec qa n d2 vec p+ vec q ;3 vec p-...

    Text Solution

    |

  14. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

    Text Solution

    |

  15. If veca ,vecb, vec c are three vectors such that veca + 2 vecb + vecc ...

    Text Solution

    |

  16. If veca and vecb are unit vectors, then find the greatest value of |ve...

    Text Solution

    |

  17. Constant forces P1= hat i+ hat j+ hat k ,P2= hat i+2 hat j- hat ka n d...

    Text Solution

    |

  18. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

    Text Solution

    |

  19. If A ,B ,C ,D are four distinct point in space such that A B is not...

    Text Solution

    |

  20. If veca=2hati+ 3hatj-5hatk,vecb =m hati+nhatj +12 hatk and veca xx vec...

    Text Solution

    |

  21. If |veca|=2, |vecb|=5 and |vecaxxvecb|=8 then find the value of veca.v...

    Text Solution

    |