Home
Class 12
MATHS
If vecu,vecv and vecw are three non copl...

If `vecu,vecv and vecw` are three non coplanar vectors then `(vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw)` equals (A) `vecu.(vecvxxvecw)` (B) `vecu.vecwxxvecv` (C) `2vecu.(vecvxxvecw)` (D) 0

A

`vecu.(vecvxxvecw)`

B

`vecu.(vecwxxvecv)`

C

`3vecu.(veccxxvecw)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`(vecu+vecv-vecw).(vecu-vecv)xx(vecv-vecw)`
`=[(vecu+vecv-vecw,vecu-vecv,vecv-vecw)]`
`=[(vecu+vecv-vecw,vecu-vecv+0vecw,0vecu+vecv-vecw)]`
`=|(1,1,-1),(1,-1,0),(0,1,-1)|[(vecu, vecv, vecw)]`
`=[(vecu, vecv, vecw)]=vecu.(vecvxxvecw)`
Promotional Banner

Topper's Solved these Questions

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|64 Videos

  • SCALAR AND VECTOR PRODUCTS OF THREE VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • SCALER AND VECTOR PRODUCTS OF TWO VECTORS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|12 Videos

Similar Questions

Explore conceptually related problems

If vecA,vecB and vecC are three non coplanar then (vecA+vecB+vecC).{(vecA+vecB)xx(vecA+vecC)} equals: (A) 0 (B) [vecA vecB vecC] (C) 2[vecA vecB vecC] (D) -[vecA vecB vecC]

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

If veca and vecb are two non collinear vectors and vecu = veca-(veca.vecb).vecb and vecv=veca x vecb then vecv is

If vecu,vecv and vecw are vectors such that vecu+vecv+vecw=vec0 then [vecu+vecv vecv+vecw vecw+vecu])= (A) 1 (B) [vecu vecv vecw] (C) 0 (D) -1

If vecu, vecv, vecw are three vectors such that [vecu vecv vecw]=1 , then 3[vecu vecv vecw]-[vecv vecw vecu]-2[vecw vecv vecu]=

Let vecu, vecv, vecw be three unit vectors such that vecu+vecv+vecw=veca,veca.vecu=3/2, veca.vecv=7/4 |veca|=2, then (A) vecu.vecv=3/2 (B) vecu.vecw=0 (C) vecu.vecw=-1/4 (D) none of these

If vec a ,\ vec b ,\ vec c are three non coplanar vectors, then ( vec a+ vec b+ vec c)dot[( vec a+ vec b)xx) vec a+ vec c)] equals [ vec a\ vec b\ vec c] b. "\ "0"\ " c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

Let vecu, vecv and vecw be three unit vectors such that vecu + vecv + vecw = veca, vecuxx (vecv xx vecw)= vecb, (vecu xx vecv) xx vecw= vecc, vec a.vecu=3//2, veca.vecv=7//4 and |veca|=2 Vector vecu is

Which of the followind expression are meanigful ? (A) vecu.(vecvxxvecw) (B) (vecu.vecv)xxvecw (C) (vecu.vecv).vecw (D) vecuxx(vecv.vecw)

Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(veca.vecb)vecb and vecv=vecaxxvecb , then |vecv| is

OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. If vecu,vecv and vecw are three non coplanar vectors then (vecu+vecv-v...

    Text Solution

    |

  2. For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc| = |v...

    Text Solution

    |

  3. Let veca=hati+hatj-hatk, vecb=hati-hatj+hatk and vecc be a unit vector...

    Text Solution

    |

  4. If veca lies in the plane of vectors vecb and vecc, then which of the ...

    Text Solution

    |

  5. The value of [(veca-vecb, vecb-vecc, vecc-veca)], where |veca|=1, |vec...

    Text Solution

    |

  6. If veca , vecb , vecc are three mutually perpendicular unit ve...

    Text Solution

    |

  7. If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr, then...

    Text Solution

    |

  8. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

    Text Solution

    |

  9. If hata, hatb, hatc are three units vectors such that hatb and hatc ar...

    Text Solution

    |

  10. For any three vectors veca, vecb, vecc the vector (vecbxxvecc)xxveca e...

    Text Solution

    |

  11. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

    Text Solution

    |

  12. For any vectors vecr the value of hatixx(vecrxxhati)+hatjxx(vecrxxha...

    Text Solution

    |

  13. If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, v...

    Text Solution

    |

  14. Let veca,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

    Text Solution

    |

  15. If vecA, vecB and vecC are three non - coplanar vectors, then (vecA.ve...

    Text Solution

    |

  16. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati+b(2)hatj+b(3)hatk an...

    Text Solution

    |

  17. If non-zero vectors veca and vecb are perpendicular to each ot...

    Text Solution

    |

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

    Text Solution

    |

  19. If veca,vecb, vecc and vecp,vecq,vecr are reciprocal system of vectors...

    Text Solution

    |

  20. vecaxx(vecaxx(vecaxxvecb)) equals

    Text Solution

    |

  21. If veca =hati + hatj, vecb = hati - hatj + hatk and vecc is a unit vec...

    Text Solution

    |