Home
Class 12
MATHS
Unit vectors veca and vecb ar perpendicu...

Unit vectors `veca and vecb` ar perpendicular , and unit vector `vecc` is inclined at an angle `theta` to both `veca and vecb . If alpha veca + beta vecb + gamma (veca xx vecb)` then.

A

`alpha = beta`

B

`gamma^(2) =1-2alpha^(2)`

C

`gamma^(2)= -cos 2theta`

D

`beta^(2) = (1+cos 2theta)/2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|60 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise LEVEL -1|90 Videos

  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

Let veca.vecb=0 where veca and vecb are unit vectors and the vector vecc is inclined an anlge theta to both veca and vecb. If vecc=mveca+nvecb + p(veca xx vecb) , (m,n,p in R) then

If veca and vecb are unit vectors inclined at an angle theta , then the value of |veca-vecb| is

Let veca and vecb are unit vectors inclined at an angle alpha to each other , if |veca+vecb| lt 1 then

Let veca be a unit vector perpendicular to unit vectors vecb and vecc and if the angle between vecb and vecc " is " alpha , " then " vecb xx vecc is

if veca, vecb and vecc are there mutually perpendicular unit vectors and veca ia a unit vector then find the value of |2veca+ vecb + vecc |^2

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: The value of sin(theta/2) is (A) 1/2 |veca-vecb| (B) 1/2|veca+vecb| (C) |veca-vecb| (D) |veca+vecb|

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If vecc is a unit vector and equal to the sum of veca and vecb the magnitude of difference between veca and vecb is (A) 1 (B) sqrt(2) (C) sqrt(3) (D) 1/sqrt(2)

Vectors veca, vecb, vecc are three unit vectors and vecc is equally inclined to both veca and vecb . Let veca xx (vecb xx vecc) + vecb xx (vecc xx veca) =(4+x^(2))vecb-(4xcos^(2)theta)veca , then veca and vecb are non-collinear vectors, x gt 0

Let veca and vecb are two vectors inclined at an angle of 60^(@) , If |veca|=|vecb|=2 ,the the angle between veca and veca + vecb is

Let veca ,vecb , vecc be three unit vectors such that angle between veca and vecb is alpha , vecb and vecc " is " beta and vecc and veca " is " gamma. " if " | veca. + vecb + vecc| =2 , then cos alpha + cos beta + cos gamma =

VMC MODULES ENGLISH-VECTORS -LEVEL -2
  1. If veca, vecb and vecc be three non-coplanar vectors and a',b' and c' ...

    Text Solution

    |

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

    Text Solution

    |

  3. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

    Text Solution

    |

  4. If I is the centre of a circle inscribed in a triangle ABC, then |vec...

    Text Solution

    |

  5. Let hata and hatb be mutually perpendicular unit vectors. Then for an...

    Text Solution

    |

  6. Let veca, vecb,vecc be unit vectors, equally inclined to each other at...

    Text Solution

    |

  7. Let veca,vecb,vecc be three non coplanar and vecdbe a vector which is ...

    Text Solution

    |

  8. If veca, vecb, vecc are unit vectors, then |veca-vecb|^2+|vecb-vecc|^2...

    Text Solution

    |

  9. Let veca, vecb and vecc be three non- coplanar vectors and vecr be any...

    Text Solution

    |

  10. If vecu and vecv be unit vectors. If vecw is a vector such that vecw+(...

    Text Solution

    |

  11. When a right handed rectangular Cartesian system OXYZ is rotated about...

    Text Solution

    |

  12. If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr...

    Text Solution

    |

  13. Given a cube ABCD A(1)B(1)C(1)D(1) which lower base ABCD, upper base A...

    Text Solution

    |

  14. Let veca, vecb, vecc be three non-zero non coplanar vectors and vecp, ...

    Text Solution

    |

  15. If veca, vecb, vecc are unit vectors such that veca. vecb=0, (veca-vec...

    Text Solution

    |

  16. I' is the incentre of DeltaABC whose corresponding sides are a,b,c res...

    Text Solution

    |

  17. Consider a tetrahedron with faces F(1),F(2),F(3),F(4). Let vec(V(1)), ...

    Text Solution

    |

  18. find all the possible triplets (a(1), a(2), a(3)) such that a(1)+a(2) ...

    Text Solution

    |

  19. In triangle ABC if bar(AB) =u/(|bar u|)-v/(|bar v|) and bar(AC)=(2bar...

    Text Solution

    |

  20. Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre...

    Text Solution

    |