Home
Class 12
MATHS
Prove that the points A (1,2,3), B(2,3,1...

Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertices of an equilateral triangle.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Prove that the points (0, 0), (3, (pi)/(2)) and (3, (pi)/(6)) are the vertices of an equilateral triangle.

Show that the points : A (0,1,2),B(2,-1,3) and C (1,-3,1) are vertices of an isosceles right angle triangle.

Show that the points (2,4,3),(4,1,9) and (10,-1,6) are the vertices of an isosceles right angled triangle.

Show that the points (1, 2, 3), (-1, -2, -1), (2, 3, 2) and (4, 7, 6) are the vertices of a parallelogram.

Show that the points : A (0,- 2), B (3, 1), C (0, 4) and D (- 3, 1) are the vertices of a square ABCD.

The points (3,2),(0,5),(-3,2) and (0,-1) are vertices of:

Prove by using the distance formula that the points A (1,2,3), B (-1, -1, -1) and C (3,5,7) are collinear.

Let A and B be two complex numbers such that A/B+B/A=1 . Prove that the origin and two points represented by A and B form the vertices of an equilateral triangle.

Find the area of the triangle fonned by the points A (1,2,4), B(3,1,-2) and C(4,3,1) as its vartices (using vector).

Show that the following sets of points are the vertices of an equilateral triangle :- (1, 1),(- 1,-1) and (-sqrt3,sqrt3) .

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. The position vectors of the points A, B, C and D are respectively 4 ha...

    Text Solution

    |

  2. Find the magnitude and components of the vector 2(-1,0,3) + 3(1,1,2)-(...

    Text Solution

    |

  3. Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertice...

    Text Solution

    |

  4. Prove that the points (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) taken in o...

    Text Solution

    |

  5. If the points (-1,-1,2),(2,m,5) and (3,11,6) are collinear, find the v...

    Text Solution

    |

  6. Using vectors, find the value of 'k' such that the points (k,-10,3),(1...

    Text Solution

    |

  7. The sides of a parallelogram represent the vectors 2 hat i- 4 hat j+ 5...

    Text Solution

    |

  8. Let vec a= 2 hat i- 2 hat j+ hat k, vec b= 2 hat i+ 3 hat j+ 6 hat k a...

    Text Solution

    |

  9. Prove that the points whose position vectors are hat i - hat j+ hat k,...

    Text Solution

    |

  10. Prove that the vectors vec a = hat i- 2 hat j+ hat k, vec b= -2 hat i+...

    Text Solution

    |

  11. Show that the points (1,1,1),(2,-1,2),(-1,2,2) and (2,2,-1) are coplan...

    Text Solution

    |

  12. Show that the points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4) are ...

    Text Solution

    |

  13. If vec a, vec b and vec c are non-coplanar (independent) vectors, prov...

    Text Solution

    |

  14. Find vec v underset 1 * vec v underset 2 when vec v underset 1= 4 hat ...

    Text Solution

    |

  15. Find vec v underset 1 * vec v underset 2 when vec v underset 1= (1,3,5...

    Text Solution

    |

  16. Find the angle between the vectors: vec v underset 1= hat i-2 hat j-...

    Text Solution

    |

  17. Find the angle between the vectors: vec v underset 1= (3,5,4) and ve...

    Text Solution

    |

  18. Find the value of lambda so that the vectors vec a= 3 hat i + 3 hat j-...

    Text Solution

    |

  19. If vec a= 2 hat i- hat j+ hat k, vec b= hat i+ hat j- 2 hat k and vec ...

    Text Solution

    |

  20. Find the value of a for which the vector 3 hat i+ 2 hat j+ 9 hat k and...

    Text Solution

    |