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|8 Videos

Similar Questions

Explore conceptually related problems

The unit vector 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

The unit vector parallel to the resultant of the vectors vec(A) = hat(i) + 2 hat(j) - hat(k) and vec(B) = 2 hat(i) + 4 hat(j) - hat(k) is

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Unit vector parallel to the resultant of vectors vec(A)= 4hat(i)-3hat(j) and vec(B)= 8hat(i)+8hat(j) will be

Find the dot product of two vectors vec(A)=3hat(i)+2hat(j)-4hat(k) and vec(B)=2hat(i)-3hat(j)-6hat(k) .

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

A unit vector in the dirction of resultant vector of vec(A)= -2hat(i)+3hat(j)+hat(k) and vec(B)= hat(i)+2hat(j)-4hat(k) is

The sine of the angle between vectors vec(a)=2hat(i)-6hat(j)-3hat(k) and vec(b)=4hat(i)+3hat(j)-hat(k)

Find the unit vectors perpendicular to the plane of the vectors vec(a) = 2 hat(i) - 6 hat(j)- 3 hat(k) and vec(b)= 4 hat(i) + 3 hat(j) - hat(k).

ALLEN-MISCELLANEOUS-Exercise-01
  1. If a unit vector is represented by 0.5 hat(i)-0.8 hat(j)+chat(k), then...

    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 physical 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 coplanar vector having different magnitudes...

    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 force vectors, one of 5 N and other of 12 N at what angl...

    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 vec(A) points verically upward and vec(B) points towards nort...

    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 resu...

    Text Solution

    |