Home
Class 12
MATHS
The formula (veca+vecb)^(2)=vec(a^(2))+v...

The formula `(veca+vecb)^(2)=vec(a^(2))+vec(b^(2))+2vecaxxvecb` is valid for non-zero vectors `vecaandvecb`.

Text Solution

Verified by Experts

`(veca+vecb)^(2)=(veca+vecb).(veca+vecb)`
`=vec(a^(2))+vec(b^(2))+2veca.vecb`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Three Dimensional Geometry|46 Videos

Similar Questions

Explore conceptually related problems

The formula (veca + vecb)^(2)= a^(-2) + vecb^(2) + 2veca xx vecb valid for non zero vectors veca and vecb .

Prove that (vecaxxvecb)^2=veca^2b^2-(veca.vecb)^2 .

The vector veca+vecb bisects the angle between the non-collinear vectors vecaandvecb , if……..

If veca and vecb are any two vectors , then prove that |vecaxxvecb|^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2)=|{:(veca.veca,veca.vecb),(veca.vecb,vecb.vecb):}| or |vecaxxvecb|^(2)+(veca.vecb)^(2)=|veca|^(2)|vecb|^(2) (This is also known as Lagrange identily)

The vector (veca-vecb)xx(veca+vecb) is equal to (A) 1/2 (vecaxxvecb) (B) vecaxxvecb (C) 2(veca+vecb) (D) 2(vecaxxvecb)

If |veca+vecb|=|veca-vecb| , then the vectors vecaandvecb are orthogonal

Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)xxvecc=1/3 |vecb||vecc|veca. if theta is the acute angle between the vectors vecb and veca then theta equals (A) 1/3 (B) sqrt(2)/3 (C) 2/3 (D) 2sqrt(2)/3

Show that the vectors 2vec a-vec b+3vec c,vec a+vec b-2vec c and vec a+vec b-3vec c are non-coplanar vectors (where vec a,vec b,vec c are non-coplanar vectors)

If veca and vec b are non-zero, non-collinear vectors such that |veca|=2, veca*vecb=1 and angle between veca and vec b is (pi)/(3) . If vecr is any vector such that vecr*veca=2, vecr*vecb=8, (vec r+2veca-10vecb)*(vecaxxvecb)=4sqrt(3) and satisfy to vecr+2veca-10vecb=lambda(veca xx vec b) , then lambda is equal to :

The position vector of foru points A,B,C,D are veca, vecb, 2veca+3vecb and veca-2vecb respectively. Expess the vectors vec(AC), vec(DB), vec(BC) and vec(CA) in terms of veca and vecb .

NCERT EXEMPLAR-VECTOR ALGEBRA-Vector Algebra
  1. For any vector veca the value of |vecaxxhati|^2+|vecaxxhatj|^2+|vecaxx...

    Text Solution

    |

  2. If |veca|=10,|vecb|=2andveca.vecb=12, then the value of |vecaxxvecb| i...

    Text Solution

    |

  3. The vectors lamdahati+hatj+2hatk,hati+lamdahatj-hatkand2hati-hatj+lamd...

    Text Solution

    |

  4. If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=0, then ...

    Text Solution

    |

  5. The projection vector of veca" on "vecb is

    Text Solution

    |

  6. If veca,vecbandvecc are three vectors such that veca+vecb+vecc=0and|ve...

    Text Solution

    |

  7. If |veca|=4and-3lelamdale2, then the range of |lamdaveca| is

    Text Solution

    |

  8. The number of vectors of unit length perpendicular to the vectors veca...

    Text Solution

    |

  9. The vector veca+vecb bisects the angle between the non-collinear vecto...

    Text Solution

    |

  10. If vecr.veca=0,vecr.vecb=0andvecr.vecc=0 for some non-zero vector vecr...

    Text Solution

    |

  11. The vectors veca=3hati-2hatj+2hatkandvecb=-hati-2hatk are the adjacent...

    Text Solution

    |

  12. The values of k, for which |k" "veca|ltveca| andk" "veca+(1)/(2)veca i...

    Text Solution

    |

  13. The value of the expression |vecaxxvecb|^(2)+(veca.vecb)^(2) is….. .

    Text Solution

    |

  14. If |vecaxxvecb|^(2)+(veca.vecb)^(2)=144and|veca|=4,"then "|vecb| is eq...

    Text Solution

    |

  15. If veca is any non-zero vector, then (veca.hati).hati+(veca.hatj).hatj...

    Text Solution

    |

  16. If |veca|=|vecb|, then necessarily it implies veca=+-vecb.

    Text Solution

    |

  17. Position vector of a point vecP is a vector whose initial point is ori...

    Text Solution

    |

  18. If |veca+vecb|=|veca-vecb|, then the vectors vecaandvecb are orthogona...

    Text Solution

    |

  19. The formula (veca+vecb)^(2)=vec(a^(2))+vec(b^(2))+2vecaxxvecb is valid...

    Text Solution

    |

  20. If vecaandvecb are adjacent sides of a rhombus, then veca.vecb=0.

    Text Solution

    |