Home
Class 12
MATHS
Consider the following inequalities in r...

Consider the following inequalities in respect of vectors `vec(a) and vec(b)`:
`1. |vec(a)+vec(b)| £|vec(a)|+|vec(b)|`
2. `|vec(a)-vec(b)|3|vec(a)|-|vec(b)|`
Which of the above is/are correct ?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
C
`|vec(a)+vec(b)|le|vec(a)|+|vec(b)|`
`|vec(a)-vec(b)|ge|vec(a)|-|vec(b)|`
both are correct.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY - RATIO & IDENTITY , TRIGONOMETRIC EQUATIONS

    NDA PREVIOUS YEARS|Exercise MCQ|238 Videos

Similar Questions

Explore conceptually related problems

Consider the following inequalities in respect of vector vec(a) and vec(b) 1. |vec(a) + vec(b)| le |vec(a)| + |vec(b)| 2. |vec(a) - vec(b)| ge |vec(a)|- |vec(b)| Which of the above is/are correct?

For any two vectors vec(a) and vec(b) consider the following statement : 1. |vec(a)+vec(b)|=|vec(a)-vec(b)|hArr vec(a), vec(b) are orthogonal. 2. |vec(a)+vec(b)|=|vec(a)|+|vec(b)|hArrvec(a), vec(b) are orthogonal. 3. |vec(a)+vec(b)|^(2)=|vec(a)|^(2)+|vec(b)|^(2)hArr vec(a),vec(b) are orthogonal. Which of the above statements is/are correct?

For non-zero vectors vec a and vec b if |vec a+vec b|<|vec a-vec b|, then vec a and vec b are

Let vec(a).vec(b) and vec(c ) be three mutually perpendicular vectors each of unit magnitude. If vec(A) = vec(a) + vec(b) + vec(c ),  vec(B) = vec(a)- vec(b) + vec(c ) and vec(C ) = vec(a) - vec(b) - vec(c ) , then which one of the following is correct?

If vec(a) and vec(b) are perpendicular vectors, |vec(a)+vec(b)|=3 and |vec(a)|=5 , find the value of |vec(b)| .

Let vec(a), vec(b) and vec(c) be three mutually perpendicular vectors each of unit magnitud. If vec(A)=vec(a)+vec(b)+vec(c), vec(B)=vec(a)-vec(b)+vec(c) and vec(C)=vec(a)-vec(b)-vec(c) , then which one of the following is correct?

Find |vec a| and |vec b|, if :(vec a+vec b)vec a-vec b=13 and |vec a|=2|vec b|

If vec(a) and vec(b) are perpendicular vectors, show that : (vec(a)+vec(b))^(2)=(vec(a)-vec(b))^(2) .

If two vectors vec a and vec b are such that |vec a|=2,|vec b|=1 and vec a*vec b=1, find (3vec a-5vec b)*(2vec a+7vec b)

NDA PREVIOUS YEARS-VECTORS -MATH
  1. If the position vector vec a at the point (5,n) is such that |vec a| =...

    Text Solution

    |

  2. If |vec(a)|=2 and |vec(b)|=3 , then |vec(a)xxvec(b)|^(2)+|vec(a).vec(b...

    Text Solution

    |

  3. Consider the following inequalities in respect of vectors vec(a) and v...

    Text Solution

    |

  4. If the magnitude of difference of two unit vectors is sqrt(3), then th...

    Text Solution

    |

  5. If the vectors alpha hat(i) + alpha hat(j) + lambda hat(k), hat(i) + h...

    Text Solution

    |

  6. The vectors vec(a), vec(b), vec(c) and vec(d) are such that vec(a)xx v...

    Text Solution

    |

  7. Let hat(a), hat(b) be two unit vectors and theta be the angle between...

    Text Solution

    |

  8. Let hat(a), hat(b) be two unit vectors and theta be the angle between...

    Text Solution

    |

  9. What is a vector of unit length orthogonal to both the vectors hat(...

    Text Solution

    |

  10. If veca, vecb, vecc are the position vectors of the vertices of an equ...

    Text Solution

    |

  11. What is the area of the parallelogram having diagonals 3hat(i) + hat(j...

    Text Solution

    |

  12. Let vec(a) = hat(i) + hat(j), vec(b) = 3 hat(i) + 4 hat(k) and vec (b)...

    Text Solution

    |

  13. Let vec(a) = hat(i) + hat(j), vec(b) = 3 hat(i) + 4 hat(k) and vec (b)...

    Text Solution

    |

  14. Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec...

    Text Solution

    |

  15. Let vec(a), vec(b) and vec(c) be three vectors such that vec(a) + vec...

    Text Solution

    |

  16. If in a right-angled triangle ABC, hypotenuse AC=p, then what is vec(A...

    Text Solution

    |

  17. Find the moment of vec F about point (2, -1, 3), where force vec ...

    Text Solution

    |

  18. If vec(a)=hat(i)-hat(j)+hat(k), vec(b) = 2 hat(i) + 3 hat( j) + 2 hat...

    Text Solution

    |

  19. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

    Text Solution

    |

  20. ABCD is a quadrilateral whose diagonals are AC and BD. Which one of th...

    Text Solution

    |