Home
Class 12
MATHS
A uni-modular tangent vector on the c...

A uni-modular tangent vector on the curve `x=t^2+2,y=4t-5,z=2t^2-6t=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)`

A

`(1)/(3)(2hati+ 2hatj+hatk)`

B

`(1)/(3) (hati-hatj-hatk)`

C

`(1)/(6)(2hati + hatj + hatk)`

D

`(2)/(3)(hati +hatj +hatk)`

Text Solution

Verified by Experts

The correct Answer is:
A
The position vector of any point at `t` is
`vecr = (2+ t^(2) ) hati + (4t -5) hatj + ( 2t^(2) -6) hatk`
`rArr (dvecr)/( dt) = 2t hai + 4hatj + ( 4t -6) hatk`
`rArr " "(dvecr)/(dt):|_(t=2) = 4hati +4hatj+2hatk`
and `" "|(dvecr)/(dt)| :|_(t=2) = sqrt(16+16+4)=4`
Hence, the required unit tangent vector at `t = 2` is
`(1)/(3) ( 2hati + 2hatj +hatk)`.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Reasoning Questions)|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Subjective)|14 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|324 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

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

Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2 hat i +4 hat j-5 hat k and hat i+2 hat j+3 hat k.Then if vec a is a unit vector parallel to AC then = (a) 1/3(3 hat i-6 hat j-2 hat k) (b) 1/3(3 hat i +6 hat j+2 hat k) (c) 1/7(3 hat i +6 hat j+2 hat k) (d) 1/7(3 hat i +6 hat j-2 hat k)

If vec a= hat i+ hat j , vec b= hat j+ hat k , vec c= hat k+ hat i , then in the reciprocal system of vectors vec a , vec b , vec c reciprocal vec a of vector vec a is a. ( hat i+ hat j+ hat k)/2 b. ( hat i- hat j+ hat k)/2 c. (- hat i- hat j+ hat k)/2 d. ( hat i+ hat j- hat k)/2

If ABCD is a parallelogram, vec A B=2 hat i+4 hat j-5 hat k and vec A D= hat i+2 hat j+3 hat k , then the unit vector in the direction of B D is 1/(sqrt(69))( hat i+2 hat j-8 hat k) (b) 1/(69)( hat i+2 hat j-8 hat k) 1/(sqrt(69))(- hat i-2 hat j+8 hat k) (d) 1/(69)(- hat i-2 hat j+8 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)

Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

A unit vector parallel to the intersection of the planes vec rdot( hat i- hat j+ hat k)=5a n d vec rdot(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))

hat i.(2hat j times3hat k)+hat j.(2hat k times3hat i)+hat k.(2hat i times3hat j) is equal to

If hat i-3 hat j+5 hat k bisects the angle between hat aa n d- hat i+2 hat j+2 hat k ,w h e r e hat a is a unit vector, then a. hat a=1/(105)(41 hat i+88 hat j-40 hat k) b. hat a=1/(105)(41 hat i+88 hat j+40 hat k) c. hat a=1/(105)(-41 hat i+88 hat j-40 hat k) d. hat a=1/(105)(41 hat i-88 hat j-40 hat k)

CENGAGE-INTRODUCTION TO VECTORS -Exercise (Single)
  1. Given three vectors veca=hati-3hatj,vecb=2hati-thatj and vecc=-2hati+2...

    Text Solution

    |

  2. If vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vec...

    Text Solution

    |

  3. In triangle A B C ,/A=30^0,H is the orthocenter and D is the midpoint ...

    Text Solution

    |

  4. Let vecr1, vecr2,……vecrn be the position of points P1,P2,………,Pn respec...

    Text Solution

    |

  5. Given three non-zero, non-coplanar vectors veca, vecb and vecc. vecr1=...

    Text Solution

    |

  6. If the vectors vec a and vec bare linearly independent and satisfying ...

    Text Solution

    |

  7. In a trapezium ABCD the vector B vec C = lambda vec(AD). If vec p = ...

    Text Solution

    |

  8. Vectors veca = hati+2hatj+3hatk, vec b = 2hati-hatj+hatk and vecc= 3ha...

    Text Solution

    |

  9. Vectors vec a=-4 hat i+3 hat k ; vec b=14 hat i+2 hat j-5 hat k are l...

    Text Solution

    |

  10. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

    Text Solution

    |

  11. If 4hati+ 7hatj+ 8hatk, 2hati+ 3hatj+ 4hatk and 2hati+ 5hatj+7hatk are...

    Text Solution

    |

  12. If vec b is a vector whose initial point divides thejoin of 5 hat ...

    Text Solution

    |

  13. The value of the lambda so that P, Q, R, S on the sides OA, OB, OC and...

    Text Solution

    |

  14. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

    Text Solution

    |

  15. Let x^2+3y^2=3 be the equation of an ellipse in the x-y plane. Aa n dB...

    Text Solution

    |

  16. Locus of the point P, for which vec(OP) represents a vector with direc...

    Text Solution

    |

  17. If vec x and vec y are two non-collinear vectors and ABC is a triangle...

    Text Solution

    |

  18. A uni-modular tangent vector on the curve x=t^2+2,y=4t-5,z=2t^2-6t=...

    Text Solution

    |

  19. If vecx and vecy are two non-collinear vectors and a, b and c represe...

    Text Solution

    |

  20. vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammad...

    Text Solution

    |