Home
Class 12
MATHS
If the vectors vec a , vec b ,a n d vec...

If the vectors ` vec a , vec b ,a n d vec c` form the sides`B C ,C Aa n dA B ,` respectively, of triangle `A B C ,t h e n` ` vec adot vec b+ vec bdot vec c+ vec cdot vec a=0` b. ` vec axx vec b= vec bxx vec c= vec cxx vec a` c. ` vec adot vec b= vec bdot vec c= vec cdot vec a` d. ` vec axx vec b+ vec bxx vec c+ vec cxx vec a=0`

A

`a*b+b*c+c*a=0`

B

`a times b=b times c=c times a`

C

`a*b=b*c=c*a`

D

`a times b=b times c=c times a=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (Level-2 Single Correct Answer Type Questions)|25 Videos
  • VECTOR ALGEBRA

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (Numerical Answer Type Questions)|25 Videos
  • VECTOR ALGEBRA

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (Concept -Based Single Correct Answer Type Questions)|10 Videos
  • TRIGONOMETRICAL IDENTITIES AND EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

If vec a, vec b, vec c are unit vectors such that vec a + vec b + vec c = vec 0 find the value of vec a * vec b + vec b * vec c + vec c * vec avec a * vec b + vec b * vec c + vec c * vec a

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

If vec a , vec b , vec c are three given non-coplanar vectors and any arbitrary vector vec r in space, where Delta1=| vec rdot vec a vec bdot vec a vec cdot vec a vec rdot vec b vec bdot vec b vec cdot vec b vec rdot vec c vec bdot vec c vec cdot vec c| , Delta2=| vec adot vec a vec rdot vec a vec cdot vec a vec adot vec b vec rdot vec b vec cdot vec b vec adot vec c vec rdot vec c vec cdot vec c| Delta3=| vec adot vec a vec bdot vec a vec rdot vec a vec adot vec b vec bdot vec b vec rdot vec b vec adot vec c vec bdot vec c vec rdot vec c| , Delta =| vec adot vec a vec bdot vec a vec cdot vec a vec adot vec b vec bdot vec b vec cdot vec b vec adot vec c vec bdot vec c vec cdot vec c| , then prove that vec r=(Delta1)/ Deltavec a+(Delta2)/Delta vec b+(Delta3)/Delta vec c .

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If the vectors vec a, vec b, vec c are coplanar, then the value of | (vec a, vec b, vec c), (vec a * vec a, vec a * vec b, vec a * vec c), (vec b * vec a, vec b * vec b, vecb * vec c) | =

Three vectors vec a , vec b , vec c satisfy the condition vec a+ vec b+ vec c= vec0 . Evaluate the quantity mu= vec adot vec b+ vec bdot vec c+ vec cdot vec a , if | vec a|=1, | vec b|=4 a n d | vec c|=2.

MCGROW HILL PUBLICATION-VECTOR ALGEBRA-SOLVED EXAMPLES (Level-1 Single Correct Answer Type Questions)
  1. Given a=i+j-k, b=-i+2j+k" and "c=-i+2j-k. A unit vector perpendicular ...

    Text Solution

    |

  2. If vec a , vec ba n d vec c are unit coplanar vectors, then the sc...

    Text Solution

    |

  3. If the vectors vec a , vec b ,a n d vec c form the sidesB C ,C Aa n d...

    Text Solution

    |

  4. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

    Text Solution

    |

  5. Let barV = 2i + j - k and barW = i + 3k If barU is a unit vector, th...

    Text Solution

    |

  6. A vector c perpendicular to the vectors 2i+3j-k" and "i-2j+3k satisfyi...

    Text Solution

    |

  7. If a, b, c be three units vectors such that a xx (b xx c)=(1/2) b ;...

    Text Solution

    |

  8. If a vector ofmagnitude 50 is collinear with vector vecb = 6 hat i - 8...

    Text Solution

    |

  9. IfA, B are two points on the curve y = x^2 in the xoy plane satisfying...

    Text Solution

    |

  10. If A, B, C, D are four points in space satisfying bar(AB).bar(CD)=K ...

    Text Solution

    |

  11. The distance of the point B with position vector i+2j+3k from the line...

    Text Solution

    |

  12. If a, b and c are unit vectors then abs(a-b)^(2)+abs(b-c)^(2)+abs(c-a)...

    Text Solution

    |

  13. Find the value of a so that the volume of the parallelepiped formed...

    Text Solution

    |

  14. If a=i-j-k,a*b=1" and "a times b=-j+k, then k is equal to

    Text Solution

    |

  15. The unit vector which is orthogonal to the vector 5i+2j+6k and is copl...

    Text Solution

    |

  16. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

  17. If abs(a)=1, abs(b)=2" and "abs(a-2b)=4" then "abs(a+3b) is equal to

    Text Solution

    |

  18. If abs(a)^(2)=8" and "a times (i+j+2k)=0 then the value of a*(-i+j+4k)...

    Text Solution

    |

  19. If a, b, c are unit vectors, then the maximum value of abs(a+2b)^(2)+a...

    Text Solution

    |

  20. Let veca=2hati+hatj-2hatk, vecb=hati+hatj. If vecc is a vector such th...

    Text Solution

    |