Home
Class 12
MATHS
If a = i + j + k, b = 4i + 3j + 4k, c = ...

If a = i + j + k, b = 4i + 3j + 4k, c = i + `alpha j + beta k` are linearly dependent and `|c| = sqrt(3)` then

A

`alpha = 1, beta = -1`

B

`alpha = 1, beta = +- 1`

C

`alpha = -1, beta = +- 1`

D

`alpha = +- 1, beta = 1`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • ADDITION OF VECTORS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 1|10 Videos

  • ADDITION OF VECTORS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 2|4 Videos

  • ADDITION OF VECTORS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 4|8 Videos

  • APPLICATIONS OF DIFFERENTIATION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-4 (SPECIAL TYPE QUESTIONS)|15 Videos

Similar Questions

Explore conceptually related problems

If a = 2i + 3j + 6k, b = 3i - 6j + 2k, c = 6i + 2j - 3k then a xx b =

If a = 2i - j + k, b = 3i + 4j - k then |a xx b| =

If a = 3i - 2j + k, b = 2i - 4j - 3k, c = -i + 2j + 2k then a + b + c =

If a = I + j - k, b = I - j + k, c = I - j - k then a xx (b xx c) =

If a = 3i - j - 2k, b = 2i + 3j + k then (a + 2b) xx (2a - b) =

If a = 2i - 3j - k, b = I + 4j - 2k then (a + b) xx (a - b) =

If a = i- 2j + k, b = 2i + j - k, c = 4i + 4j + 3k then |(a xx b) xx c| =

If a = i - j + 2k, b = 2i + 3j + k, c = i - k , then magnitude of a + 2b-3c is

If a = i + j - 2k, b = -i + 2j + k, c = i - 2j + 2k, then a unit vector parallel to a + b + c =

DIPTI PUBLICATION ( AP EAMET)-ADDITION OF VECTORS -EXERCISE 1
  1. The vectors 3a - 2b - 4c, -a + 2c, - 2a + b + 3c are

    Text Solution

    |

  2. If the vectors 2a - b + c, a + 2b - 3c, 3a + mb + 5c are linearly depe...

    Text Solution

    |

  3. If a = i + j + k, b = 4i + 3j + 4k, c = i + alpha j + beta k are linea...

    Text Solution

    |

  4. If a = i + 4j, b = 2i - 3j and c = 5i + 9j then c =

    Text Solution

    |

  5. If a = 2i - j + 3k, b = -i + 4j - 2k, c = 5i + j + 7k and xa + yb = c ...

    Text Solution

    |

  6. The linear relation between the vectors a + 3b + 4c, a - 2b + 3c, a + ...

    Text Solution

    |

  7. The values of lambda such that (x, y, z) ne (0, 0, 0) and (i + j + 3k)...

    Text Solution

    |

  8. If the position vectors of A, B are 2a + 3b - c, 4a - b + 5c, then the...

    Text Solution

    |

  9. If the position vectors of A, B are i + j + k and i + j - 4k repective...

    Text Solution

    |

  10. If A = i + 2j + 3k and B = 2i - j + 4k, then the position vectors of t...

    Text Solution

    |

  11. A point C = (5a + 4b - 5c)/(3) divides the line joining A = a - 2b + 3...

    Text Solution

    |

  12. The ratio in which i + 2j + 3k divides the join of -2i + 3j + 5k and 7...

    Text Solution

    |

  13. If A = i + 2j + 3k, B = 2i + 4j + 7k and C = 2i + 3j + 5k are collinea...

    Text Solution

    |

  14. The ratio in which the line segment joining the points with position v...

    Text Solution

    |

  15. If the position vectors of A, B are i + 2j - 3k, 3i - 2j + 5k respecti...

    Text Solution

    |

  16. If the position vectors of A, B are 2a - 3b, 3a + 2b respectively then...

    Text Solution

    |

  17. The position vectors of P and Q are respectively a and b. If R is a po...

    Text Solution

    |

  18. If the vectors AB = -3i + 4k and AC = 5i - 2j + 4k are the sides of a ...

    Text Solution

    |

  19. If the position vectors of A, B, C are 2i - 2j + k, 2i + j - k, -2i + ...

    Text Solution

    |

  20. The position vector of a point lying on the line joining the points wh...

    Text Solution

    |