Home
Class 12
MATHS
Show that the points (2,3,4), (-1,-2,1),...

Show that the points (2,3,4), (-1,-2,1), (5,8,7) are colinear

Text Solution

Verified by Experts

The correct Answer is:
Let the given points be A, B and C respectively.
Then the direction ration of AB are -1, -2, -2, -3, 1-4 i.e., -3, -5, -3 and the direction ratios of AB are 5, -2, 8-3, 7-4 i.e., 3, 5, 3
Since `(-3)/3=(-5)/5=(-3)/5`, the direction ratios of AB and AC are proportional. Thus A, B and C are collinear
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|86 Videos

  • VECTOR ALGEBRA

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|161 Videos

Similar Questions

Explore conceptually related problems

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

(ii)Show that the points (-1,-1),(2,3) and (8,11) are collinear.

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

Using vectors, show that the points A(1,2,7),B(2,6,3),C(3,10,-1) are collinear.

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 A (2,-3,4), B(-1,2,1) and C (0, 1/3 ,2) are collinear.

Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7)are collinear and find the ratio in which B divides AC.

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

Prove that the points '(1,3),(2,5)' '(3,7)' are on the same line.

Show that the points A(1,2,7),B(2,6,3) "and" C(3,10,-1) are collinear.

A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
  1. Find the direction cosine of a line which makes equal angles with the...

    Text Solution

    |

  2. If a line has the direction ratios '-18,(12) ,-4', then what are its d...

    Text Solution

    |

  3. Show that the points (2,3,4), (-1,-2,1), (5,8,7) are colinear

    Text Solution

    |

  4. Find the direction cosines of the sides of the triangle whose vertices...

    Text Solution

    |

  5. Find direction cosines of the line passing through the poins P(-2, 4, ...

    Text Solution

    |

  6. Show that the three lines with direction cosines (12)/13, (-3)/13, (-4...

    Text Solution

    |

  7. Show that the line through the points (1,-1,2), (3,4,-2) is perpendicu...

    Text Solution

    |

  8. Find the equation of the line through the points (-1, -2, 1) and (1, 2...

    Text Solution

    |

  9. Find the equation of the line which passes through the point '(1,2,3)'...

    Text Solution

    |

  10. Find the equation of the line in vector and in cartesian form that pas...

    Text Solution

    |

  11. Find the cartersian equation of the line which passes through the poin...

    Text Solution

    |

  12. The cartestian equation of a line is (x-5)/3=(y+4)/7=(z-6)/2. Write it...

    Text Solution

    |

  13. Find the vector and the cartesian equation of the lines that passes th...

    Text Solution

    |

  14. Find the vector and the cartesian equations of the lines that passes t...

    Text Solution

    |

  15. Find the angle between the pair lines barr=2i-5j+k+lambda(3i+2j+6k) ...

    Text Solution

    |

  16. Find the angle between the following pairs of lines.vecr = 3hati+hatj-...

    Text Solution

    |

  17. Find the angles between the lines (x-2)/2=(y-1)/5=(z+3)/-3 and (x+...

    Text Solution

    |

  18. Find the angle between the following pairs of lines.(x)/2=(y)/2=(z)/1 ...

    Text Solution

    |

  19. Find the values of p so that the lines (1-x)/3 = (7y-14)/(2p) = (z-3)/...

    Text Solution

    |

  20. Find the shortest distance between the lines whose vector equations ...

    Text Solution

    |