Home
Class 11
MATHS
If side vec A B of an equilateral trang...

If side ` vec A B` of an equilateral trangle `A B C` lying in the x-y plane `3 hat i ,` then side ` vec C B` can be a. `-3/2( hat i-sqrt(3) hat j)` b. `3/2( hat i-sqrt(3) hat j)` c. `-3/2( hat i+sqrt(3) hat j)` d. `3/2( hat i+sqrt(3) hat j)`

A

`-3/2(hati- sqrt3hatj)`

B

`-3/2(hati- sqrt3hatj)`

C

`-3/2(hati + sqrt3hatj)`

D

`3/2(hati + sqrt3hatj)`

Text Solution

Verified by Experts

The correct Answer is:
b,d
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE PUBLICATION|Exercise All Questions|689 Videos

Similar Questions

Explore conceptually related problems

If the vectors hat i- hat j , hat j+ hat k and vec a form a triangle, then vec a may be a. - hat i- hat k b. hat i-2 hat j- hat k c. 2 hat i+ hat j+ hat k d. hat i+ hat k

Vectors perpendicular to hat i- hat j- hat k and in the plane of hat i+ hat j+ hat ka n d- hat i+ hat j+ vec k are hat i+ hat k b. 2 hat i+ hat j+ hat k c. 3 hat i+2 hat j+ hat k d. -4 hat i-2 hat j-2 hat k

Let vec a=2 hati+hat j+ hat k , vec b=hat i+2hat j- hatk and a unit vector vec c be coplanar. If vec c is perpendicular to vec a , then vec c is a. 1/(sqrt(2))(-hat j+hat k) b. 1/(sqrt(3))(-hat i-hat j-hat k)"" c. 1/(sqrt(5))(-hat k-2 hat j) d. 1/(sqrt(3))(hat i-hat j- hat k)

A unit vector parallel to the intersection of the planes vec r. \ ( hat i- hat j+ hat k)=5 \ a n d \ vec r. \ (2 hat i+ hat j-3 hat k)=4 a. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) b. (-2 hat i+5 hat j-3 hat k)/(sqrt(38)) c. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) d. (-2 hat i-5 hat j-3 hat k)/(sqrt(38))

The scalar projection of vec(a) = 2 hat (i) - 3hat(j) + hat (k) on vec (b) = 3 hat(i) - 6 hat (j) - 2 hat (k)

The position vectors of the points Pa n dQ with respect to the origin O are vec a= hat i+3 hat j-2 hat k and vec b=3 hat i- hat j-2 hat k , respectively. If M is a point on P Q , such that O M is the bisector of angleP O Q , then vec O M is a. 2( hat i- hat j+ hat k) b. 2 hat i+ hat j-2 hat k c. 2(- hat i+ hat j- hat k) d. 2( hat i+ hat j+ hat k)

Find the area of the parallelogram whose adjacent sides are vec (a) = 3 hat (i) - hat(j) + 4 hat (k) and vec(b) = hat (i) - hat (j) + hat (k)

If vec (a) = 2 hat (i) - 3 hat (j) + 4 hat (k) and vec(b) = - 6 hat (i) + 9 hat (j) - 12 hat (k) , then

A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6 at t=2 is a. 1/3(2 hat i+2 hat j+ hat k) b. 1/3( hat i- hat j- hat k) c. 1/6(2 hat i+ hat j+ hat k) d. 2/3( hat i+ hat j+ hat k)

Let vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k be three vectors. A vector vec v in the plane of vec a a n d vec b , whose projection on vec c is 1/(sqrt(3)) is given by a. hat i-3 hat j+3 hat k b. -3 hat i-3 hat j+3 hat k c. 3 hat i- hat j+3 hat k d. hat i+3 hat j-3 hat k

CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. A vector vec d is equally inclined to three vectors vec a= hat i+ ...

    Text Solution

    |

  2. Vectors perpendicular to hat i- hat j- hat k and in the plane of hat...

    Text Solution

    |

  3. If side vec A B of an equilateral trangle A B C lying in the x-y plan...

    Text Solution

    |

  4. Let hata be a unit vector and hatb a non zero vector non parallel to v...

    Text Solution

    |

  5. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector ...

    Text Solution

    |

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

    Text Solution

    |

  7. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

    Text Solution

    |

  8. if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 ...

    Text Solution

    |

  9. vec ba n d vec c are unit vectors. Then for any arbitrary vector vec ...

    Text Solution

    |

  10. If vec a , vec b , a n d harr c are three unit vecrtors such that ...

    Text Solution

    |

  11. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

    Text Solution

    |

  12. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

    Text Solution

    |

  13. The scalars l and m such that l vec a+m vec b= vec c ,where vec a , v...

    Text Solution

    |

  14. If (veca xx vecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of ...

    Text Solution

    |

  15. A ,B ,Ca n dD are four points such that vec A B=m(2 hat i-6 hat j+2 h...

    Text Solution

    |

  16. If the vectors vec a, vec b, vec c are non-coplanar and l,m,n are dist...

    Text Solution

    |

  17. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

    Text Solution

    |

  18. If vectors vec A=2 hat i+3 hat j+4 hat k , vec B= hat i+ hat j+5 hat ...

    Text Solution

    |

  19. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc=...

    Text Solution

    |

  20. If veca xx (vecbxx vecc)= (veca xx vecb)xxvecc then

    Text Solution

    |