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

Prove that the points (2, -1, 3), (1, 2, -1), (3, 4, 5) and (0, -7, -2) are co-planar. Also find the equation of the plane containing these points.

Text Solution

Verified by Experts

The correct Answer is:
13x-y-4z-15=0
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 1 MARK (TYPE-I: MULTIPLE CHOICE QUESTIONS )|40 Videos

  • THREE DIMENSIONAL GEOMETRY

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 1 MARK (TYPE-II: FILL IN THE BLANKS QUESTIONS)|21 Videos

  • SAMPLE QUESTIONS PAPER - III (UNSOLVED)

    ACCURATE PUBLICATION|Exercise SECTION - D|6 Videos

  • VECTOR ALGEBRA

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 2 MARKS|102 Videos

Similar Questions

Explore conceptually related problems

Show that the four points S(0,-1,0), B(2,1,-1), C(1,1,1) and D(3,3,0) are coplanar. Find the equation of the plane containing them.

Show that the four points : (0,-1,1),(4,5,1),(3,9,4),(-4,4,4) are coplanar. Also find the equation of the plane containing them.

Show that the points (1,-1,1),(2,3,1),(1,2,3) and (0,-2,3) are coplanar. Find the equation of the plane in which they lie.

Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5)/5 are coplanar. Also find the equation of the plane containing the lines.

Show that the lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-2)/3=(y-3)/4=(z-4)/5 are coplanar. Also find the equation of the plane containing the lines.

Prove that the points (1,2,3),(4,0,4),(-2,4,2) and (7,-2,5) are collinear.

Prove that the points (1,- 6), (5, 2), (7, 0) and (- 1,-4) are concyclic. Find the radius of the circle.

Prove that the points (2, - 1), (0, 2), (3, 3) and (5,0) are the vertices of a parallelogram. Also find the angle between its diagonals.

Find the equation of the plane containing the points (1,0,0),(0,2,0) and (0,0,3).

Prove that the following points are collinear : (- 2, 3, 5), (1, 2, 3), (7, 0, - 1).

ACCURATE PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTIONS CARRYING 6 MARKS:
  1. Prove that the points (2, -1, 3), (1, 2, -1), (3, 4, 5) and (0, -7, -2...

    Text Solution

    |

  2. Find the direction cosines of a line which makes equal angles with the...

    Text Solution

    |

  3. If the equations of a line AB are (3-x)/1 = (y+2)/-2 = (z-5)/4, then t...

    Text Solution

    |

  4. If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4, w...

    Text Solution

    |

  5. Find the vector equation of a line passing through (2, -1, 1) and para...

    Text Solution

    |

  6. Find the vector equation of the line through the point (2,-1,-1) and i...

    Text Solution

    |

  7. Find the point on the line (x+2)/(3)=(y+1)/(2)=(z-3)/(2) at a distance...

    Text Solution

    |

  8. Find the coordinates of the point where the line through (3, 4, 1) and...

    Text Solution

    |

  9. Find the coordinates of the point where the line through (3, – 4, – 5)...

    Text Solution

    |

  10. Find the value of p so that the lines : l1:(1-x)/3=(7y-14)/(2p)=(z-3)/...

    Text Solution

    |

  11. Find the vector and cartesian equation of a line through the point (1,...

    Text Solution

    |

  12. Find the vector and cartesian equation of the line passing through the...

    Text Solution

    |

  13. Find the equation of the line passing through the point (2, -1, 3) and...

    Text Solution

    |

  14. Find the equation of a line passing through the points A(0, 6, -9) and...

    Text Solution

    |

  15. Find the image of the point (1,6,3) in the line : x/1=(y-1)/2=(z-2)/3.

    Text Solution

    |

  16. Find the co ordinates of the foot of perpendicular and the length of t...

    Text Solution

    |

  17. Find the shortest distance between the lines : vecr=hati-hatj+lamda(...

    Text Solution

    |

  18. Find the shortest distance between the following lines whose vector eq...

    Text Solution

    |

  19. Find the shortest distance between the lines vecr=hati+2hatj+3hatk+lam...

    Text Solution

    |

  20. Find the shortest distance (S.D.) between the lines : vecr=hatj+lamd...

    Text Solution

    |

  21. Write the vector equation of the following lines and hence find distan...

    Text Solution

    |