Home
Class 11
MATHS
If veca and vecb are unit vectors such t...

If `veca and vecb` are unit vectors such that `(veca +vecb). (2veca + 3vecb)xx(3veca - 2vecb)=vec0` then angle between `veca and vecb` is

A

0

B

`pi//2`

C

`pi`

D

indeterminate

Text Solution

Verified by Experts

The correct Answer is:
d
`vec0 = (veca + vecb) . (2veca + 3vecb) xx ( 3veca -2 vecb)`
` = (veca + vecb ) . (-4 veca xx vecb - 9 veca xx vecb)`
`= - 13 (veca + vecb) . (veca xx vecb)`
Which is true for all values of `veca and vecb`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Multiple Question)|11 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.3|18 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|320 Videos

Similar Questions

Explore conceptually related problems

If veca and vecb are unequal unit vectors such that (veca -vecb) xx [(vecb+veca) xx (2veca+vecb)]=veca+vecb , then angle theta between veca and vecb can be

If veca and vecb are two vectors such that |veca|=1, |vecb|=4, veca.vecb=2 . If vecc=(2veca xx vecb)-3vecb , then the angle between veca and vecc is

If veca,vecb are two unit vectors such that |veca + vecb| = 2sqrt3 and |veca -vecb|=6 then the angle between veca and vecb , is

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

If |veca - vecb|=|veca| =|vecb|=1 , then the angle between veca and vecb , is

If veca , vecb are unit vectors such that |vec a+vecb|=-1 " then " |2veca -3vecb| =

If |veca.vecb|= |veca xx vecb| , then the angle between veca and vecb is

if veca , vecb ,vecc are three vectors such that veca +vecb + vecc = vec0 then

Let veca and vecb be two vectors such that |2 veca + 3 vecb| = |3 veca + vecb| and the angle between veca and vecb is 60^(@) . If 1/8 veca is a unit vector, then |vecb| is equal to :

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. The position vectors of points A,B and C are hati+hatj,hati + 5hatj -h...

    Text Solution

    |

  2. Given three vectors eveca, vecb and vecc two of which are non-collinea...

    Text Solution

    |

  3. If veca and vecb are unit vectors such that (veca +vecb). (2veca + 3ve...

    Text Solution

    |

  4. If in a right-angled triangle A B C , the hypotenuse A B=p ,t h e n...

    Text Solution

    |

  5. Resolved part of vector veca and along vector vecb " is " veca1 and th...

    Text Solution

    |

  6. Let veca=2hati=hatj+hatk, vecb=hati+2hatj-hatk and vecc=hati+hatj-2hat...

    Text Solution

    |

  7. If P is any arbitrary point on the circumcirlce of the equllateral ...

    Text Solution

    |

  8. If vecr and vecs are non-zero constant vectors and the scalar b is cho...

    Text Solution

    |

  9. veca and vecb are two unit vectors that are mutually perpendicular. A...

    Text Solution

    |

  10. Given that veca,vecb,vecp,vecq are four vectors such that veca + vecb...

    Text Solution

    |

  11. The position vectors of the vertices A, B and C of a triangle are thre...

    Text Solution

    |

  12. If a is real constant A ,Ba n dC are variable angles and sqrt(a^2-4)ta...

    Text Solution

    |

  13. The vertex A triangle A B C is on the line vec r= hat i+ hat j+lambda...

    Text Solution

    |

  14. A non-zero vecto veca is such tha its projections along vectors (hati ...

    Text Solution

    |

  15. Position vector hat k is rotated about the origin by angle 135^0 i...

    Text Solution

    |

  16. ln a quadrilateral ABCD, vec(AC) is the bisector of the (vec(AB) ^^ v...

    Text Solution

    |

  17. In fig. 2.33 AB, DE and GF are parallel to each other and AD, BG and E...

    Text Solution

    |

  18. Vectors hata in the plane of vecb = 2 hati +hatj and vecc = hati-hatj ...

    Text Solution

    |

  19. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D a...

    Text Solution

    |

  20. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

    Text Solution

    |