Home
Class 12
MATHS
Find the cartesian equation fo the follo...

Find the cartesian equation fo the following planes. `vecr.(hati+hatj-hatk)=2`

Text Solution

Verified by Experts

The correct Answer is:
Replacing `vecr` by `xhati+yhatj+zhatk` we have `(xhati+yhatj+zhatk).(hati+hatj+hatk) = 2` i.e., x+yz=2, which is the cartesian equation of the plane
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

Find the cartesian equation fo the following planes. vecr.(2hati+3hatj-4hatk)=1

Find the cartesian equation fo the following planes. vecr.[(s-2t)hati+(3-t)hatj+(2s-t)hatk] = 15

Find the angle between the following pairs of lines. vecr = 3hati+hatj-hatk+lambda(hati-hatj-hatk) vecr = 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the angle between the following pairs of lines: i) vecr=2 hati-5 hatj+hatk+lambda(3 hati+2 hatj+6 hatk) and vecr=7 hati-6 hatk+mu(hati+2 hatj+2 hatk) (ii) vecr=3 hati+hatj-2 hatk+lambda(hati-hatj-2 hatk) and vecr=2 hati-hatj-5 6 hatk+mu(3 hati-5 hatj-4 hatk)

Find the equation of the plane passing through the line of intersection of the planes vecr .(hati+hatj+hatk)=1 and vecr.(2 hati+3 hatj-hatk)+4=0 and parallel to x -axis.

Find the shortest distance between the lines vecr =(2hati-hatj-hatk)+lambda(3hati-5hatj+2hatk) and vecr =(hati+hatj+hatk)+mu(hati-hatj+hatk)

Find the equation of the plane which contains the line of intersection of the planes vecr .(hati+2 hatj+3 hatk)-4 =0 , vecr .(2 hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr .(5 hati+3 hatj-6 hatk)+8=0

A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
  1. Determine the direction cosines of the normal to the plane and the d...

    Text Solution

    |

  2. Find the vector equation of a plane which is at a distance of 7 units ...

    Text Solution

    |

  3. Find the cartesian equation fo the following planes. vecr.(hati+hatj-h...

    Text Solution

    |

  4. Find the cartesian equation fo the following planes.vecr.(2hati+3hatj-...

    Text Solution

    |

  5. Find the cartesian equation fo the following planes. vecr.[(s-2t)hati+...

    Text Solution

    |

  6. Find the co-ordinates of the foot of the perpendicular drawn from th...

    Text Solution

    |

  7. In the following cases, find the co-ordinates of the foot of the perpe...

    Text Solution

    |

  8. Find the co-ordinates of the foot of the perpendicular drawn from th...

    Text Solution

    |

  9. Find the co-ordinates of the foot of the perpendicular drawn from the ...

    Text Solution

    |

  10. Find the vector and cartesian equations of the plane that passes throu...

    Text Solution

    |

  11. Find the vector and cartesian equations of the plane that passes throu...

    Text Solution

    |

  12. Find the equation of the planes that pass through the points.. (1, 1,...

    Text Solution

    |

  13. Find the equation of the planes that pass through the points... (1, ...

    Text Solution

    |

  14. Find the intercepts cut off by the plane 2x + y - z = 5

    Text Solution

    |

  15. Find the equation of the plane with intercept 3 on the y-axis and para...

    Text Solution

    |

  16. Find the equation of the plane through the intersection of the planes ...

    Text Solution

    |

  17. Find the vector equation of the plane passing through the intersection...

    Text Solution

    |

  18. Find the equation of the plane through the line of intersection of the...

    Text Solution

    |

  19. Find the angle between the planes whose vector equations are vecr.(2h...

    Text Solution

    |

  20. Determine whether the given planes are parallel or perpendicular and i...

    Text Solution

    |