Home
Class 11
MATHS
If vecp, vecq , vecr denote vectors vecb...

If `vecp, vecq , vecr` denote vectors `vecbxxvecc, vecc xx vecc xx veca, vecaxx vecb`. Respectively, show that `veca` is parallel to `vecq xx vecr , vecb` is parallel to `vecrxx vecp , vecc` is parallel to `vecp xx vecq`.\

Text Solution

AI Generated Solution

To show that the vectors \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \) are parallel to the respective cross products as stated in the question, we can follow these steps: ### Step 1: Define the vectors Let: - \( \vec{p} = \vec{b} \times \vec{c} \) - \( \vec{q} = \vec{c} \times \vec{a} \) - \( \vec{r} = \vec{a} \times \vec{b} \) ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise single correct answer type|28 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.2|15 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos
  • LIMITS AND DERIVATIVES

    CENGAGE ENGLISH|Exercise All Questions|691 Videos

Similar Questions

Explore conceptually related problems

if veca + vecb + vecc=0 , then show that veca xx vecb = vecb xx vecc = vecc xx veca .

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Solve the vector equation vecr xx vecb = veca xx vecb, vecr.vecc = 0 provided that vecc is not perpendicular to vecb

If veca, vecb,vecc are three non-coplanar vectors such that veca xx vecb=vecc,vecb xx vecc=veca,vecc xx veca=vecb , then the value of |veca|+|vecb|+|vecc| is

If veca, vecb, vecc are the unit vectors such that veca + 2vecb + 2vecc=0 , then |veca xx vecc| is equal to:

If vectors, vecb, vecc and vecd are not coplanar, the prove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=vecc .

CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.3
  1. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

    Text Solution

    |

  2. If vecl,vecm,vecn are three non coplanar vectors prove that [vec vecm ...

    Text Solution

    |

  3. if the volume of a parallelpiped whose adjacent egges are veca=2hati+3...

    Text Solution

    |

  4. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

    Text Solution

    |

  5. If vecx . Veca =0, vecx. Vecb=0 and vecx. vecc=0 for some non-zero vec...

    Text Solution

    |

  6. If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the v...

    Text Solution

    |

  7. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

    Text Solution

    |

  8. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove...

    Text Solution

    |

  9. Prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vec...

    Text Solution

    |

  10. for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecax...

    Text Solution

    |

  11. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

    Text Solution

    |

  12. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

    Text Solution

    |

  13. Let veca, vecb and vecc be non-zero vectors such that no two are colli...

    Text Solution

    |

  14. If vecp, vecq , vecr denote vectors vecbxxvecc, vecc xx vecc xx veca, ...

    Text Solution

    |

  15. Let veca, vecb , vecc be non -coplanar vectors and let equations veca'...

    Text Solution

    |

  16. Given unit vectors hatm hatn and hatp such that angle between hatm and...

    Text Solution

    |

  17. vec a , vec b ,a n d vec c are three unit vectors and every two are...

    Text Solution

    |

  18. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

    Text Solution

    |