Home
Class 11
PHYSICS
Given |vec(A)(1)|=2,|vec(A)(2)|=3 and |v...

Given `|vec(A)_(1)|=2,|vec(A)_(2)|=3` and `|vec(A)_(1)+vec(A)_(2)|=3`. Find the value of `(vec(A)_(1)+2vec(A)_(2)).(3vec(A)_(1)-4vec(A)_(2))`.

A

-64

B

60

C

-60

D

64

Text Solution

Verified by Experts

The correct Answer is:
A
`A_(1)=2, A_(2)=3,|vec(A)_(1)+vec(A)_(2)|=3`
`rArr|vec(A)_(1)+vec(A)_(2)|^(2)=9`
`rArr A_(1)^(2)+A_(2)^(2)+2vec(A)_(1).vec(A)_(2)=9`
`rArr 2^(2)+3^(2)+2vec(A)_(1).vec(A)_(2)=9 rArr vec(A)_(1).vec(A)_(2)= -2`
Now, `(vec(A)_(1)+2vec(A)_(2)).(3vec(A)_(1)-4vec(A)_(2))= 3A_(1)^(2)-8A_(2)^(2)+2vec(A)_(1).vec(A)_(2)`
`3(2)^(2)- 8(3)^(2)+2(-2)=-64`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise Multiple Correct|5 Videos

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise Subjective|28 Videos

  • TRAVELLING WAVES

    CENGAGE PHYSICS|Exercise Integer|9 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Archives (integer)|4 Videos

Similar Questions

Explore conceptually related problems

If |vec(V)_(1)+vec(V)_(2)|=|vec(V)_(1)-vec(V)_(2)|and V_(2) is finite, then

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

If vec A_(1) and vec A_(2) are two non-collinear unit vectors and if |vec A_(1)+vec A_(2)|=sqrt(3) then the value of (vec A_(1)-vec A_(2))*(2vec A_(1)+vec A_(2)) is

If |vec a|=2,|vec b|=1 and vec a*vcb=1 then find the value of (3vec a-5vec b)*(2vec a+vec 7vec b)

Consider the following statements in respect of the vectors vec(u)_(1)= (1, 2, 3), vec(u)_(2)= (2, 3, 1) vec(u)_(3)= (1, 3,2) and vec(u)_(4)= (4,6,2) I vec(u)_(1) is parallel to vec(u)_(4) II. vec(u)_(2) is parallel to vec(u)_(4) III. vec(u)_(3) is parallel to vec(u)_(4) Which of the statements given above are correct?

If |vec(a)|=2 and |vec(b)|=3 , then |vec(a) xx vec(b)|^(2)+ |vec(a).vec(b)|^(2) is equal to

If vec e_(1),vec e_(2),vec e_(3) and vec E_(1),vec E_(2),vec E_(3) are two sets of vectors such that vec e_(i)*vec E_(j)=1, if i=j and vec e_(i)*vec E_(j)=0 and if i!=j then prove that [vec e_(1)vec e_(2)vec e_(3)][vec E_(1)vec E_(2)vec E_(3)]=1

If vec(A) = 3 hati +2hatj and vec(B) = hati - 2hatj +3hatk , find the magnitudes of vec(A) +vec(B) and vec(A) - vec(B) .

(vec a xxvec b)^(2)+(vec a*vec b)^(2)=144 and |vec a|=4 then find the value of |vec b|

The base vectors vec a_ (1), vec a_ (2), vec a_ (3) are given in terms vectors vec b_ (1), vec b_ (2), vec b_ (3) vec a_ (1) = 2vec b_ (1) + 3vec b_ (1) -vec b_ (1), vec a_ (2) = vec a_ (1) -2vec b_ (2) + 2vec b_ (3), vec a_ (3) = - 2vec b_ ( 1) + vec b_ (2) -2vec b_ (3) if vec F_ (1) = 3vec b_ (1) -vec b_ (2) + 2vec b_ (3), Express vec F in terms of vec a_ (1) , vec a_ (2), vec a_ (3)

CENGAGE PHYSICS-VECTORS-Exercise Single Correct
  1. If |vec(A)+vec(B)|=|vec(A)|=|vec(B)| then the angle between vec(A) and...

    Text Solution

    |

  2. If vector vec(A)=hat(i)+2hat(j)+4hat(k) and vec(B)=5hat(i) represent t...

    Text Solution

    |

  3. Given |vec(A)(1)|=2,|vec(A)(2)|=3 and |vec(A)(1)+vec(A)(2)|=3. Find th...

    Text Solution

    |

  4. Three vector vec(A),vec(B), vec(C ) satisfy the relation vec(A)*vec(B)...

    Text Solution

    |

  5. If vec(A)=vec(B)+vec(C ), and the magnitudes of vec(A),vec(B),vec(C ) ...

    Text Solution

    |

  6. Given: vec(A)=Acos theta hat(i)+Asin theta hat(j). A vector vec(B), wh...

    Text Solution

    |

  7. The angle which the vector vec(A)=2hat(i)+3hat(j) makes with the y-axi...

    Text Solution

    |

  8. Given vec(P)=3hat(i)-4hat(j). Which of the following is perpendicular ...

    Text Solution

    |

  9. In going from one city to another, a car travles 75km north, 60km noth...

    Text Solution

    |

  10. What is the angle between vec(A) and vec(B), If vec(A) and vec(B) are ...

    Text Solution

    |

  11. Two vectors vec(a) and vec(b) are such that |vec(a)+vec(b)|=|vec(a)-ve...

    Text Solution

    |

  12. Given vec(A)=4hat(i)+6hat(j) and vec(B)=2hat(i)+3hat(j). Which of the ...

    Text Solution

    |

  13. Given vec(A)=2hat(i)+phat(j)+qhat(k) and vec(B)=5hat(i)+7hat(j)+3hat(k...

    Text Solution

    |

  14. If vec(A) is perpendicular to vec(B), then

    Text Solution

    |

  15. If the angle between the vectors vec(a) and vec(b) is an acute angle, ...

    Text Solution

    |

  16. Given that vec(A)+vec(B)=vec(C ). If |vec(A)|=4, |vec(B)|=5 and |vec(C...

    Text Solution

    |

  17. If vec(b)=3hat(i)+4hat(j) and vec(a)=hat(i)-hat(j) the vector having t...

    Text Solution

    |

  18. Choose the wrong statement.

    Text Solution

    |

  19. What displacement at an angle 60^(@) to the x-axis has an x-component ...

    Text Solution

    |

  20. Mark the correct statement.

    Text Solution

    |