Home
Class 12
MATHS
The three points whose position vectors ...

The three points whose position vectors are i+2j+3k, 3i+4j+7k, and -3i-2j-5k

A

form the vertices of an equilateral triangle

B

form the vertices of a right angled triangle

C

are collinear

D

form the vertices of an isosceles triangle

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|194 Videos

Similar Questions

Explore conceptually related problems

The position vector of a point laying on the line joining the points whose position vectors are i+j-k and i-j+k is

If the points whose position vectors are 60i+3j, 40i-8j and li-52j are collinear then I =

The values of 'a' for which the points A, B, C with position vectors 2i-j+k, i-3j-5k and ai-3j+k respectively are the vertices of a right angled triangle with C = pi/2 are

Let alpha, beta, gamma are distinct real numbers. The points with position vectors alpha i + beta j + gamma k , beta i + gamma j + alpha k , gamma i + alpha j + beta k

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

The area pf the triangle whose two sides are given by 4i - j + k and 3i+j - k is

Show that four points A,B,C and D with position vectors 4i+5j+k,-(j+k),3i+9j+4k and -4i+4j+4k respectively coplanar.

HIMALAYA PUBLICATION-VECTORS AND THEIR APPLICATIONS-QUESTION BANK
  1. If alpha and beta are two nonzero and different vectors such that |vec...

    Text Solution

    |

  2. If vec a = i + lambda j + k, vec b = i+j+k, then for |vec a + vec b| =...

    Text Solution

    |

  3. The three points whose position vectors are i+2j+3k, 3i+4j+7k, and -3i...

    Text Solution

    |

  4. If vec a = i + 2j+3k, vec b = i-2j+k, vec c = 4i+3j-2k and vec a + lam...

    Text Solution

    |

  5. If vec a and vec b are unit vectors |vec a xx vec b| =1 then the angle...

    Text Solution

    |

  6. If |vec(a)| = 3, |vec(b) = 4 and |vec(a) + vec(b)| = 1, then |vec(a) -...

    Text Solution

    |

  7. If the position vectors of A and B are 3i-2j+k and 2i+4j+3k then |vec ...

    Text Solution

    |

  8. If vec a and vec b are unit vectors such that |vec a xx vec b| = vec a...

    Text Solution

    |

  9. (vec b xx vec c) xx (vec c xx vec a ) =

    Text Solution

    |

  10. If vec a = 2i+3j-4k, vec b = i + j +k and vec c = 4i+2j+3k, then |vec...

    Text Solution

    |

  11. If theta is the angle between the vectors 2i-2j+4k and 3i+j+2k then si...

    Text Solution

    |

  12. If two out of the three vectors vec a, vec b, vec c are unit vectors, ...

    Text Solution

    |

  13. (sin theta+i cos theta)^(9)=

    Text Solution

    |

  14. If OACB is a parallelogram with vec OC = vec a and vec AB = vec b then...

    Text Solution

    |

  15. If vec a, vec b, vec c, vec d are the coplanar vectors then (vec a xx ...

    Text Solution

    |

  16. With usual notation [i-j j-k k-i] =

    Text Solution

    |

  17. If theta is the angle between any two vector vec a and vec b, then |ve...

    Text Solution

    |

  18. If vec a = i +j and vec b = j-k then the angle between vec a + vec b a...

    Text Solution

    |

  19. ABCD is a parallelogram, with AC, BD as diagonals. Then vec AC - vec B...

    Text Solution

    |

  20. If vec a = i+j+k, vec b = i+j, vec c = i and (vec a xx vec b) xx vec c...

    Text Solution

    |