Home
Class 11
PHYSICS
The unit vactor parallel to the resultan...

The unit vactor parallel to the resultant of the vectors `vec(A)=4hat(i)+3hat(j)+6hat(k)` and `vec(B)=-hat(i)+3hat(j)-8hat(k)` is :-

A

`1/7 (3hat(i)+6hat(j)-2hat(k))`

B

`1/7 (3hat(i)+6hat(j)+2hat(k))`

C

`1/49 (3hat(i)+6hat(j)+2hat(k))`

D

`1/49(3hat(i)+6hat(j)-2hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
A
Required unit vector
`=(vec(A)+vec(B))/(|vec(A)+vec(B)|)=(3hat(i)+6hat(j)-2hat(k))/sqrt(3^(2)+6^(2)+2^(2))=1/7 (3i+ 6hat(j)-2hat(k))`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN |Exercise Exersice-03|7 Videos

  • MISCELLANEOUS

    ALLEN |Exercise ASSERTION-REASON|18 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Part -II Example Some worked out Examples|1 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN |Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise EXERCISE-IV|7 Videos

Similar Questions

Explore conceptually related problems

Angle between the vectors vec(a)=-hat(i)+2hat(j)+hat(k) and vec(b)=xhat(i)+hat(j)+(x+1)hat(k)

Find the angle between vec(P) = - 2hat(i) +3 hat(j) +hat(k) and vec(Q) = hat(i) +2hat(j) - 4hat(k)

Find a unit vector perpendicular to both the vectors (2hat(i)+3hat(j)+hat(k)) and (hat(i)-hat(j)-2hat(k)) .

The compenent of vec(A)=hat(i)+hat(j)+5hat(j) perpendicular to vec(B)=3hat(i)+4hat(j) is

If vec(A) =2hat(i)-2hat(j) and vec(B)=2hat(k) then vec(A).vec(B) ……

Find the components of vector vec(a)=3hat(i)+4hat(j) along the direction of vectors hat(i)+hat(j) & hat(i)-hat(j)

A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(i)+hat(j)-hat(k) then the plane containing them is

The projection of a vector vec(r )=3hat(i)+hat(j)+2hat(k) on the x-y plane has magnitude

Statemen-I The locus of a point which is equidistant from the point whose position vectors are 3hat(i)-2hat(j)+5hat(k) and (hat(i)+2hat(j)-hat(k)), is r.(hat(i)-2hat(j)+3hat(k))=8. Statement-II The locus of a point which is equidistant from the points whose position vectors are a and b is |r-(a+b)/(2)|*(a-b)=0 .

What is the length of projection of vec(A)=3hat(i)+4hat(j)+5hat(k) on xy plane ?

ALLEN -MISCELLANEOUS-Exercise-01
  1. If a unit vector represented by 0.5hati-0.8hatj+chatk, then the value ...

    Text Solution

    |

  2. Force 3N, 4N and 12 N act at a point in mutually perpendicular directi...

    Text Solution

    |

  3. The unit vactor parallel to the resultant of the vectors vec(A)=4hat(i...

    Text Solution

    |

  4. A physcial quantity which has a direction

    Text Solution

    |

  5. The following sets of three vectors act on a body. Whose resultant can...

    Text Solution

    |

  6. How many minimum number of vectors in different planes can be added to...

    Text Solution

    |

  7. The resultant of two vectors vec(P) and vec(Q) is vec(R). If vec(Q) is...

    Text Solution

    |

  8. Figure shows three vectors vec(a), vec(b) and vec(c), where R is the m...

    Text Solution

    |

  9. A displacement vector, at an angle of 30^(@) with y-axis has an x-comp...

    Text Solution

    |

  10. I started walking down a road in morning facing the sun. After walking...

    Text Solution

    |

  11. A bird moves from point (1 m, -2 m, 3 m) to (4 m, 2 m, 3 m). If the sp...

    Text Solution

    |

  12. Any vector in an arbitrary direction can always be replaced by two (or...

    Text Solution

    |

  13. There are two forces vectors, one of 5N and other of 12N at what angle...

    Text Solution

    |

  14. A particle has displacement of 12m towards east and 5 m towards north ...

    Text Solution

    |

  15. 21 coplanar non collinear forces (all of equal magnitude) maintain a b...

    Text Solution

    |

  16. A vector vecA points vertically upward and vecB points towards north. ...

    Text Solution

    |

  17. If |vec(A)xxvec(B)|=sqrt(3)vec(A).vec(B), then the value of |vec(A)+ve...

    Text Solution

    |

  18. The projection of vec(A) on vec(B) is :-

    Text Solution

    |

  19. Given that P=Q=R. If vec(P)+vec(Q)=vec(R) then the angle between vec(P...

    Text Solution

    |

  20. At what angle must the two forces (X+y) and (x-y) act so that the re...

    Text Solution

    |