Home
Class 12
MATHS
If vecalpha+ vecbeta+ vecgamma=a vecdel...

If ` vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vecdelta=b vecalpha, vecalphaa n d vecdelta` are non-colliner, then ` vecalpha+ vecbeta+ vecgamma+ vecdelta` equals a. `a vecalpha` b. `b vecdelta` c. `0` d. `(a+b) vecgamma`

A

`a vecalpha `

B

`b vecdelta`

C

`0`

D

`(a+ b)vecgamma`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `vecalpha + vecbeta + vecgamma = a vecdelta" "` (i)
`" "vecbeta + vecgamma + vecdelta = b vecalpha" "` (ii)
From (i), ` vecalpha + vecbeta + vecdelta = (a+1) vecdelta" "` (iii)
From (ii), `vecalpha + vecbeta + vecgamma + vecdelta = (b+1)vecalpha " "` (iv)
From (iii) and (iv), we get
`" "(a+1) vecdelta = (b+1) vecalpha " "` (v)
Since `vecalpha` is not parallel to `vecdelta`,
From (v), `a=1 =0 and b+1 =0`
From (iii), `vecalpha + vecbeta + vecgamma + vecdelta =0`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Reasoning Questions)|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Subjective)|14 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

If alpha+beta+gamma= a vecdelta and vecbeta+vecgamma+vecdelta = b vecalpha and alpha, vecbeta, vecgamma are non coplanar and vecalpha is not parallel to vecdelta then vecalpha+vecbeta+vecgamma+vecdelta equals (A) avecalpha (B) bvecdelta (C) 0 (D) (a+b)vecgamma

let vecalpha=i+2j-k , vecbeta=2i-j+3k , vecgamma=2i+j+6k be three vectors . fi vecalpha and vecbeta are both perpendicular to the vecdelta and vecdelta.vecgamma=10, then what is the magnitude of vecdelta

vecalpha and vecbeta are two unit vectos and vecr is a vector such that vecr,vecalpha=0 and sqrt(2)(vecrxxvecbeta)=3(vecrxxvecalpha)-vecbeta , then (1)/(|vecr|^(2)) equal

If vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvecgamma)= (A) |vecalpha|^2(vecbeta.vecgamma) (B) |vecbeta|^2(vecgamma.vecalpha) (C) |vecgamma|^2(vecalpha.vecbeta) (D) |vecalpha||vecbeta||vecgamma|

If a(vecalphaxxvecbeta)=b(vecbetaxxvecgamma)+c(vecgammaxxvecalpha)=vec0 and at least one of a,b and c is non zero then vectors vecalpha, vecbeta, vecgamma are (A) parallel (B) coplanar (C) mutually perpendicular (D) none of these

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

Findthe value of vecalphaxx(vecbetaxxvecgamma) , where, vecalpha=2veci-10vecj+2veck, vecbeta=3veci+vecj+2veck, vecgamma =2veci+vecj+3veck

If veca,vecb,vecc are mutually perpendicular vector and veca=alpha(vecaxxvecb)+beta(vecbxxvecc)+gamma(veccxxveca) and [veca vecb vecc]=1 then vecalpha+vecbeta+vecgamma= (A) |veca|^2 (B) -|veca|^2 (C) 0 (D) none of these

If vecalpha is a constant vectro and vecgamma is the position vector of a variable point (x,y,z), show that (vecgamma-vecalpha) vecalpha =0 is the equation of a plane through fixed point vec(alpha)

Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j such that vecalpha= vec a+ vec b+ vec c Then the resolution of the vector vecalpha into components with respect to vec aa n d vec b is given by a. 3 vec a-2 vec b b. 3 vec b-2 vec a c. 2 vec a-3 vec b d. vec a-2 vec b

CENGAGE-INTRODUCTION TO VECTORS -Exercise (Single)
  1. let us define , the length of a vector as |a| + |b| +|c| . this defini...

    Text Solution

    |

  2. Given three vectors veca=hati-3hatj,vecb=2hati-thatj and vecc=-2hati+2...

    Text Solution

    |

  3. If vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vec...

    Text Solution

    |

  4. In triangle A B C ,/A=30^0,H is the orthocenter and D is the midpoint ...

    Text Solution

    |

  5. Let vecr1, vecr2,……vecrn be the position of points P1,P2,………,Pn respec...

    Text Solution

    |

  6. Given three non-zero, non-coplanar vectors veca, vecb and vecc. vecr1=...

    Text Solution

    |

  7. If the vectors vec a and vec bare linearly independent and satisfying ...

    Text Solution

    |

  8. In a trapezium ABCD the vector B vec C = lambda vec(AD). If vec p = ...

    Text Solution

    |

  9. Vectors veca = hati+2hatj+3hatk, vec b = 2hati-hatj+hatk and vecc= 3ha...

    Text Solution

    |

  10. Vectors vec a=-4 hat i+3 hat k ; vec b=14 hat i+2 hat j-5 hat k are l...

    Text Solution

    |

  11. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

    Text Solution

    |

  12. If 4hati+ 7hatj+ 8hatk, 2hati+ 3hatj+ 4hatk and 2hati+ 5hatj+7hatk are...

    Text Solution

    |

  13. If vec b is a vector whose initial point divides thejoin of 5 hat ...

    Text Solution

    |

  14. The value of the lambda so that P, Q, R, S on the sides OA, OB, OC and...

    Text Solution

    |

  15. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

    Text Solution

    |

  16. Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB...

    Text Solution

    |

  17. Locus of the point P, for which vec(OP) represents a vector with direc...

    Text Solution

    |

  18. If vec x and vec y are two non-collinear vectors and ABC is a triangle...

    Text Solution

    |

  19. A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6t=...

    Text Solution

    |

  20. If vecx and vecy are two non-collinear vectors and a, b and c represe...

    Text Solution

    |