Home
Class 12
MATHS
If veca,vecb,vecc,vecd are four distinct...

If `veca,vecb,vecc,vecd` are four distinct vectors satisfying the conditions `vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxecd` then prove that `veca.vecb+vecc.vecd!=veca.vecc+vecb.vecd`

Promotional Banner

Topper's Solved these Questions

  • VECTOR

    MOTION|Exercise EXERCISE - 4 ( LEVEL -I)|36 Videos

  • TRIGONOMETRIC EQUATION

    MOTION|Exercise EXERCISE 4|10 Videos

Similar Questions

Explore conceptually related problems

If veca, vecb, vecc and vecd ar distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

If vecaxxvecb = veccxxvecd and vecaxxvecc = vecbxxvecd , show that (veca-vecd) is parallel to (vecb-vecc) .

If veca.vecb=veca.vecc, vecaxxvecb=vecaxxvecc and veca!=vec0, then prove that vecb=vecc.

If the vectors veca, vecb, vecc, vecd are any four vectors, then (vecaxxvecb).(veccxxvecd) is equal to

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|

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|

If veca,vecb,vecc,vecd are unit vectors such that veca.vecb=1/2 , vecc.vecd=1/2 and angle between veca xx vecb and vecc xx vecd is pi/6 then the value of |[vecavecbvecd]vecc-[vecavecbvecc]vecd|=

veca,vecb,vecc are non zero vectors. If vecaxxvecb=vecaxxvecc and veca.vecb=veca.vecc then show that vecb=vecc .

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecaxx(vecbxx(veccxxvecd)))=(vecb.vecd)[veca vecc vecd]

MOTION-VECTOR -EXERCISE - 4 ( LEVEL-II)
  1. A unit vector int eh plane of the vectors 2hati+hatj+hatk, hati-hatj+h...

    Text Solution

    |

  2. If veca=veci+vecj+veck, veca.vecb=1 and vecaxxvecb=vecj-veck, then vec...

    Text Solution

    |

  3. If veca,vecb,vecc,vecd are four distinct vectors satisfying the condit...

    Text Solution

    |

  4. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk andvecc= hathatj-h...

    Text Solution

    |

  5. Let vecA be a vector parallel to the of intersection of planes P1 and ...

    Text Solution

    |

  6. The number of distinct values of lamda, for which the vectors -lamda^(...

    Text Solution

    |

  7. Let veca, vecb ,vecc be unit vetors such that veca + vecb + vecc = ve...

    Text Solution

    |

  8. Assertion: vec(PQ)xx(vec(RS)+vec(ST))!=0, Reason : vec(PQ)xxvec(RS)=ve...

    Text Solution

    |

  9. The edges of a parallelopiped are of unit length and are parallel to n...

    Text Solution

    |

  10. Lelt two non collinear unit vectors hata and hatb form and acute angle...

    Text Solution

    |

  11. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

    Text Solution

    |

  12. Let P, Q, R and S be the points on the plane with position vectors -2h...

    Text Solution

    |

  13. If veca and vecb are vectors in space given by veca=(hati-23hatj)/(sqr...

    Text Solution

    |

  14. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

    Text Solution

    |

  15. The vectors which is/are coplanar with vectors hati+hatj+2hatk and hat...

    Text Solution

    |

  16. Let veca=-hati-hatk, vecb=-hati+hatj and vecc=hati+2hatj+3hatk be th...

    Text Solution

    |

  17. Let bar(PR)=3hati+hatj-2hatk and bar(SQ)=hati-3hatj-4hatk determine d...

    Text Solution

    |

  18. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

    Text Solution

    |

  19. Let vecx,vecy and vecz be three vector each of magnitude sqrt(2) an...

    Text Solution

    |

  20. Let veca, vecb and vecc be non - coplanar unit vectors, equally inclin...

    Text Solution

    |