Home
Class 12
MATHS
If veca is any non-zero vector, then (ve...

If `veca` is any non-zero vector, then `(veca.hati).hati+(veca.hatj).hatj+(veca.veck)hatk` is equal to …….

Text Solution

Verified by Experts

Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk`
`:.veca.hati=a_(1),veca.hatj=a_(2)andveca.hatk=a_(3)`
`:.(veca.hati)hati+(veca.hatj)hatj+(veca.hatk)hatk=a_(1)hati+a_(2)hatj+a_(3)hatk=veca`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Three Dimensional Geometry|46 Videos

Similar Questions

Explore conceptually related problems

(veca hati)hati + (veca hatj)hatj + (veca hatk) hatk is value of :

(veca.hati)(vecaxxhati)+(veca.hatj)+(veca.hatk)(vecaxxhatk) is equal to

Prove that for any vector veca , veca=(veca. hati)hati+(veca. hatj)hatj+(veca. hatk)hatk ,

If veca,vecb are non-collinear vectors, then [(veca,vecb,hati)]hati+[(veca,vecb,hatj)]hatj+[(veca,vecb,hatk)]hatk=

If veca vecb are non zero and non collinear vectors, then [(veca, vecb, veci)]hati+[(veca, vecb, vecj)]hatj+[(veca, vecb, veck)]hatk is equal to

{veca.(vecbxxhati)}hati+{veca.(vecbxxhatj)}hatj+{veca.(vecbxxhatk)}hatk=

If veca=hati+hatj+hatk and vecb=hati-hatj then the vector (veca.hati)hati+(veca.hatj)hatj+(veca.hatk)hatk,(vecb.hati)hati+(vecb.hatj)hatj+(vecb.hatk)hatk and hati+hatj-2hatk (A) are mutually perpendicular (B) are coplanasr (C) form a parallelopiped of volume 6 units (D) form as parallelopiped of volume 3 units

For any vector veca |veca xx hati|^(2) + |veca xx hatj|^(2) + |veca xx hatk|^(2) is equal to

Statement 1: If veca, vecb are non zero and non collinear vectors, then vecaxxvecb=[(veca, vecb, hati)]hati+[(veca, vecb, hatj)]hatj+[(veca, vecb, hatk)]hatk Statement 2: For any vector vecr vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk

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

    |