Home
Class 11
MATHS
If hat a , hat b ,a n d hat c are three...

If ` hat a , hat b ,a n d hat c` are three unit vectors inclined to each other at angle `theta,` then the maximum value of `theta` is `pi/3` b. `pi/4` c. `(2pi)/3` d. `(5pi)/6`

A

`pi/3`

B

`pi/2`

C

`(2pi)/3`

D

`(5pi)/5`

Text Solution

Verified by Experts

The correct Answer is:
c
`(hata+hatb + hatc)^(2)ge0`
`3+2(hata.hatb+vecb.hatc+vecc.veca)ge0`
` 3 + 6 cos theta ge 0`
`cos theta ge - 1/2`
`Rightarrow theta= (2pi)/3`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE ENGLISH|Exercise All Questions|691 Videos

Similar Questions

Explore conceptually related problems

If hat a and hatb are two unit vectors inclined at an angle theta , then sin(theta/2)

If hat aa n d hat b are unit vectors inclined at an angle theta , then prove that sintheta/2=1/2| hat a- hat b|dot

If hat a\ a n d\ hat b are unit vectors inclined at an angle theta then prove that tantheta/2=(| hat a- hat b|)/(| hat a+ hat b|)

If \ vec a\ a n d\ vec b are two unit vectors inclined at an angle theta such that |a+b|,1, then theta (2pi)/3 c. pi/3

If hat a , hat b ,a n d hat c are unit vectors, then | hat a+hat b|^2+| hat b- hat c|^2+| hat c- hat a|^2 does not exceed

If hat a , hat b ,a n d hat c are three unit vectors, such that hat a+ hat b+ hat c is also a unit vector and theta_1,theta_2a n dtheta_3 are angles between the vectors hat a , hat b ; hat b , hat ca n d hat c , hat a respectively, then among theta_1,theta_2,a n dtheta_3dot a. all are acute angles b. all are right angles c. at least one is obtuse angle d. none of these

If vec a\ a n d\ vec b be two unit vectors and theta is the angle between them. Then vec a+ vec b\ is an unit vector, if theta= pi/2 b. (2pi)/3 c. pi/4 d. pi/3

L_1a n dL_2 and two lines whose vector equations are L_1: vec r=lambda((costheta+sqrt(3)) hat i+(sqrt(2)sintheta) hat j+(costheta-sqrt(3)) hat k) L_2: vec r=mu(a hat i+b hat j+c hat k) , where lambdaa n dmu are scalars and alpha is the acute angel between L_1a n dL_2dot If the angel alpha is independent of theta, then the value of alpha is a. pi/6 b. pi/4 c. pi/3 d. pi/2

If hat a and hat b are unit vectors inclined at an angle theta , then prove that costheta/2=1/2| hat a+ hat b| tantheta/2=1/2|( hat a- hat b)/( hat a+ hat b)|

If (costheta+cos2theta)^3=cos^3theta+cos^3 2theta, then the least positive value of theta is equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

CENGAGE ENGLISH-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
  1. P (vecp) and Q (vecq) are the position vectors of two fixed points and...

    Text Solution

    |

  2. Two adjacent sides of a parallelogram ABCD are 2hati+4hatj -5 hatkand ...

    Text Solution

    |

  3. If hat a , hat b ,a n d hat c are three unit vectors inclined to ea...

    Text Solution

    |

  4. Let the pair of vector veca,vecb and vecc,veccd each determine a plane...

    Text Solution

    |

  5. If vecr.veca=vecr.vecb=vecr.vecc=0 " where "veca,vecb and vecc are non...

    Text Solution

    |

  6. If veca satisfies vecaxx(hati+2hatj+hatk)=hati-hatk" then " veca is eq...

    Text Solution

    |

  7. Vectors 3veca-5vecb and 2veca + vecb are mutually perpendicular. If ve...

    Text Solution

    |

  8. The units vectors orthogonal to the vector - hat i + 2hat j + 2hat k ...

    Text Solution

    |

  9. The value of x for which the angle between veca = 2x^(2) hati + 4x h...

    Text Solution

    |

  10. If vectors veca and vecb are two adjacent sides of parallelograsm then...

    Text Solution

    |

  11. A parallelogram is constructed on 3veca+vecb and veca-4vecb, where |ve...

    Text Solution

    |

  12. Let veca.vecb=0 where veca and vecb are unit vectors and the vector ve...

    Text Solution

    |

  13. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

    Text Solution

    |

  14. Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lam...

    Text Solution

    |

  15. A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2...

    Text Solution

    |

  16. Let P be a point interior to the acute triangle A B Cdot If P A+P B...

    Text Solution

    |

  17. G is the centroid of triangle ABC and A1 and B1 are the midpoints of s...

    Text Solution

    |

  18. Points veca , vecb vecc and vecd are coplanar and (sin alpha)veca + (2...

    Text Solution

    |

  19. If veca and vecb are any two vectors of magnitudes 1and 2. respectivel...

    Text Solution

    |

  20. If veca and vecb are any two vectors of magnitude 2 and 3 respective...

    Text Solution

    |