Home
Class 12
MATHS
Show that the points A (2, -3, -4), B (...

Show that the points `A (2, -3, -4)`, `B (1, 2, 3)`and `C (3, -8, -11)`are collinear.

Text Solution

AI Generated Solution

To show that the points A(2, -3, -4), B(1, 2, 3), and C(3, -8, -11) are collinear, we need to demonstrate that the vectors AB and BC are parallel. This can be done by showing that the direction ratios of these vectors are proportional. ### Step-by-step Solution: 1. **Find the coordinates of vectors AB and BC:** - The vector AB can be found using the formula: \[ \overrightarrow{AB} = B - A = (1 - 2, 2 - (-3), 3 - (-4)) ...
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise Exercise 11.1|5 Videos
  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 11.3|14 Videos
  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|23 Videos
  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 1.3|14 Videos
  • VECTOR ALGEBRA

    NCERT ENGLISH|Exercise Exercise 10.5|7 Videos

Similar Questions

Explore conceptually related problems

Using section formula, show that the points A (2, -3, 4) , B (-1, 2, 1) and C(0,1/3,2) are collinear.

Using section formula, show that the points (2, -3, 4), (-1, 2,1) and (0, (1)/(3) , 2) are collinear.

Using section formula, prove that the three points A (-2,3,5), B (1,2,3) and C (7,0,-1) are collinear.

Show that the points (2, -3, 3), (1, 2, 4) and (3, -8, 2) are collinear. [Hint : Sum of any two sides is equal to third side.]

Show that the points P (-2, 3, 5) , Q (1, 2, 3) and R (7, 0, -1) are collinear.

Show that the points A (2, 3, 4), B (3, 4, 6) and C (5, 6, 16) are collinear.

Using section formula, show that the points A(2,-3,4),\ B(-1,2,1)\ a n d\ C(0,1/3,2)\ are collinear.

Using section formaul, show that the points (2, -1, 3), (0, 1, 2) and (2/3, 1/3, 7/3) are collinear.

Using section formula, show that the points A(1, 2, 1), B(2, 1, 0) and c(7/5, 8/5, 3/5) are collinear.

Using the section formula, prove that the three points A(-2,3,5),B(1,2,3) and C(7,0,-1) are collinear.

NCERT ENGLISH-THREE DIMENSIONAL GEOMETRY-SOLVED EXAMPLES
  1. Find the vector equation for the line passing through the points (1, 0...

    Text Solution

    |

  2. Find the vector and the Cartesian equations of the line through the p...

    Text Solution

    |

  3. Show that the points A (2, -3, -4), B (1, 2, 3)and C (3, -8, -11)ar...

    Text Solution

    |

  4. Find the direction cosines of x, y and z-axis.

    Text Solution

    |

  5. Find the direction cosines of the line passing through the two points...

    Text Solution

    |

  6. If a line has direction ratios 2,1,2.determine its direction cosines.

    Text Solution

    |

  7. If a line makes angle 90^@, 60^@and 30^@with the positive direction ...

    Text Solution

    |

  8. Find the angle between the pair of lines given by vecr=3 hat i+2 ha...

    Text Solution

    |

  9. The Cartesian equation of a line is (x+3)/2=(y-5)/4=(z+6)/2. Find th...

    Text Solution

    |

  10. Show that the lines (x+3)/(-3)=(y-1)/1=(z-5)/5and (x+1)/(-1)=(y-2)/2=(...

    Text Solution

    |

  11. Find the vector equation of the plane passing through the intersectio...

    Text Solution

    |

  12. Find the angle between the two planes 3x - 6y + 2z = 7and 2x + 2y-2z ...

    Text Solution

    |

  13. Find the angle between the two planes 2x + y-2z = 5and 3x- 6y-2z = 7...

    Text Solution

    |

  14. Find the distance of a point (2, 5, 3)from the plane vecr.(6 hat i-...

    Text Solution

    |

  15. Find the angle between the pair of lines (x+3)/3=(y-1)/5=(z+3)/4and (x...

    Text Solution

    |

  16. Find the shortest distance between the lines l1 and l2 whose vector ...

    Text Solution

    |

  17. Find the distance between the lines l1and l2given by vec r= hat i+2 ...

    Text Solution

    |

  18. Find the vector equation of the plane which is at a distance of 6/(sqr...

    Text Solution

    |

  19. Find the direction cosines of the unit vector perpendicular to the pla...

    Text Solution

    |

  20. Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin.

    Text Solution

    |