Home
Class 12
MATHS
The points A(4, 5, 10), B(2, 3, 4) and C...

The points `A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1)` are three vertices of a parallelogram ABCD, then

A

Vector equation of AB is `2i+3j+4k+lambda(i+j+3k)`

B

Cartesian equation of BC is `(x-2)/(1)=(y-3)/(1)=(z-4)/(-5)`

C

Coordinate of D are `(3, 4,5)`

D

ABCD is a rectangle.

Text Solution

Verified by Experts

The correct Answer is:
(a,b, c)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|36 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|96 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

The points A(4,5,10),B(2,3,4) and C(1,2,-1) are three vertices of a parallelogram ABCD. Find the vector equations of the sides AB and BC and also find the coordinates of point D.

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

Using slopes, prove that the points A(-2,-1) , B(1,0) , C(4,3) and D(1,2) are the vertices of a parallelogram.

If the points A(a,-11),quad B(5,b),quad C(2,15) and D(1,1) are the vertices of a parallelogram ABCD, find the values of a and b

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(1,2),B(4,3),C(1,0) and D(-2,-1) are the vertices of a parallelogram.

If the points A(1,-2),B(2,3),C(-3,2) and D(-4,-3) are the vertices of parallelogram ABCD, then taking AB as the base,find the height of the parallelogram.

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 ABCD but not a rectangle.

Show that the points A(1,0),B(5,3),C(2,7) and D(-2,4) are the vertices of a parallelogram.

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (More Than One Correct Option Type Questions)
  1. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve x^2+y^2=r...

    Text Solution

    |

  2. A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(...

    Text Solution

    |

  3. Consider the plane through (2, 3, -1) and at right angles to the vecto...

    Text Solution

    |

  4. A plane passes through a fixed point (a, b, c) and cuts the axes in A,...

    Text Solution

    |

  5. Let A be vector parallel to line of intersection of planes P1 and P2. ...

    Text Solution

    |

  6. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

    Text Solution

    |

  7. If p1, p2, p3 denote the perpendicular distance of the plane 2x-3y+4z+...

    Text Solution

    |

  8. A line segment has length 63 and direction ratios are 3, -26. The comp...

    Text Solution

    |

  9. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

    Text Solution

    |

  10. The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices ...

    Text Solution

    |

  11. The lines x=y=z meets the plane x+y+z=1 at the point P and the sphere ...

    Text Solution

    |

  12. A rod of length 2units whose one end is (1, 0, -1) and other end touch...

    Text Solution

    |

  13. Consider the planes p1: 2x+y+z+4=0, p2: y-z+4=0 and p3: 3x+2y+z+8=0 ...

    Text Solution

    |

  14. The volume of a tetrahedron prism ABCA1B1C1 is equal to 3. Find the co...

    Text Solution

    |

  15. If the plane passing through the origin and parallel to the line (x-1)...

    Text Solution

    |

  16. Let OABC be a regular tetrahedron with side length unity, then its vol...

    Text Solution

    |

  17. The OABC is a tetrahedron such that OA^2+BC^2=OB^2+CA^2=OC^2+AB^2,then

    Text Solution

    |

  18. If the line (x)/(1)=(y)/(2)=(z)/(3) intersects the line 3beta^2x+3(1-2...

    Text Solution

    |

  19. Let PM be the perpendicular from the point P(1, 2, 3) to XY-plane. If ...

    Text Solution

    |

  20. A variable plane which remains at a constant distance P from the orig...

    Text Solution

    |