Home
Class 12
MATHS
Length of the perpendicular from origin ...

Length of the perpendicular from origin to the
plane passing through the three non-collinear
points `veca, vecb, vecc` is

A

`([veca vecb vecc])/(abs(vecaxxvecb + vecbxxvecc+veccxxveca))`

B

`(3[veca vecb vecc])/(abs(vecaxxvecb + vecbxxvecc+veccxxveca))`

C

`[veca vecb vecc]`

D

`([veca vecb vecc]^(2))/(abs(vecaxxvecb + vecbxxvecc+veccxxveca))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - C|14 Videos
  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - D COMPREHENSION I|3 Videos
  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - A|90 Videos
  • STRAIGHT LINES

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos
  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Section - J (Akash Challengers Question)|16 Videos

Similar Questions

Explore conceptually related problems

The length of the perpendicular from the origin to the plane passing though three non-collinear points veca,vecb,vecc is

The length of the perpendicular from the origin to the plane passing though three non-collinear points veca,vecb,vecc is

The length of the perpendicular from the origin to the plane passing through the points veca and containing the line vecr = vecb + lambda vecc is

Show that the equation of as line perpendicular to the two vectors vecb and vecc and passing through point veca is vecr=veca+t(vecbxxvecc) where t is a scalar.

Prove that the perpendiculasr distanceof as point with position vector veca from the plane thorugh three points with position vectors vecb,vecc, vecd is ([veca vecc vecd]+[veca vecd vecb]+[veca vecb vecc]-[vecb vecc vecd])/(|vecbxxvecc+veccxxvecd+vecdxvecb|)

veca,vecb and vecc are three non-zero vectors, no two of which are collinear and the vectors veca+vecb is collinear with vecc , vecb+vecc is collinear with veca , then veca+vecb+vecc=

If veca, vecb,vecc are unit vectors such that veca is perpendicular to the plane of vecb, vecc and the angle between vecb,vecc is pi/3 , then |veca+vecb+vecc|=

If veca, vecb, vecc, vecd are the position vectors of points A, B, C and D , respectively referred to the same origin O such that no three of these points are collinear and veca+vecc=vecb+vecd , then prove that quadrilateral ABCD is a parallelogram.

The perpendicular distance of the point vecc from the joining veca and vecb is

veca, vecb ,vecc are three non zero vectors no two of which are collonear and the vectors veca + vecb be collinear with vecc,vecb+vecc to collinear with veca then veca+vecb+vecc the equal to ? (A) veca (B) vecb (C) vecc (D) None of these

AAKASH INSTITUTE ENGLISH-THREE DIMENSIONAL GEOMETRY -ASSIGNMENT SECTION - B
  1. The equation of the plane which passes through the points (2, 1, -1)...

    Text Solution

    |

  2. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

    Text Solution

    |

  3. Length of the perpendicular from origin to the plane passing through...

    Text Solution

    |

  4. If the plane x- 3y +5z= d passes through the point (1, 2, 4), then the...

    Text Solution

    |

  5. The plane x / 2 + y / 3 + z / 4 = 1 cuts the co-ordinate axes in A, B,...

    Text Solution

    |

  6. The position vectors of points A and B are hati - hatj + 3hatk and 3h...

    Text Solution

    |

  7. The vector equation of the plane through the point (2, 1, -1) and pass...

    Text Solution

    |

  8. Find the vector equation of line passing through the point (1,2,-4)...

    Text Solution

    |

  9. The line x + 2y - z - 3 = 0 = x + 3y - 2 - 4 is parallel to

    Text Solution

    |

  10. The shortest distance between the lines 2x + y + z - 1 = 0 = 3x + y + ...

    Text Solution

    |

  11. The lines x + y + z - 3 = 0 = 2x - y + 5z - 6 and x - y - z + 1 = 0 = ...

    Text Solution

    |

  12. The line vecr= veca + lambda vecb will not meet the plane vecr cdot ...

    Text Solution

    |

  13. The plane vecr cdot vecn = q will contain the line vecr = veca + lambd...

    Text Solution

    |

  14. Two system of rectangular axes have the same origin. IF a plane cuts t...

    Text Solution

    |

  15. Find the length of the perpendicular from the point (1,2,3) to the ...

    Text Solution

    |

  16. A variable plane which remains at q constant distance 3p from the orig...

    Text Solution

    |

  17. The planes 2x + 5y + 3z = 0, x-y+4z = 2 and7y-5z + 4 = 0

    Text Solution

    |

  18. Let vecn be a unit vector perpendicular to the plane containing the ...

    Text Solution

    |

  19. The coordinates of the point P on the line vecr=(hati+hatj+hatk)+lamda...

    Text Solution

    |

  20. The projection of the line segment joining the Points (1, 2, 3) and ...

    Text Solution

    |