Home
Class 12
MATHS
Show that the points P(hati-hatj+3hatk) ...

Show that the points `P(hati-hatj+3hatk)` and `Q(3hati+3hatj+3hatk)` are equidistant from the plane `vecr.(5hati+2hatj-7hatk)+9=0` and lie on opposite sides of it.

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

  • RELATIONS AND FUNCTIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|401 Videos

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

Similar Questions

Explore conceptually related problems

Show that the points : A(-2hati+3hatj+5hatk), B(hati+2hatj+3hatk) and C(7hati-hatk) are collinear.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line : (2hati+3hatj+4hatk)+lambda(2hati+3hatj+4hatk) and the plane : vecr*(hati+hatj+hatk)=5 .

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2hatj+4hatk) and the plane vecr.(2hati+hatj-3hatk)+4=0

True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies in the plane vecr.(3hati+hatj-hatk)-2=0 .

Find the image of the point hati+3hatj+4hatk in the plane vecr.(2hati-hatj+hatk)+3=0 .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Show that the equation of the plane through the line x/l=y/m=z/n and p...

    Text Solution

    |

  2. Two systems of rectangular axes have the same origin. If a plane cuts ...

    Text Solution

    |

  3. Show that the points P(hati-hatj+3hatk) and Q(3hati+3hatj+3hatk) are e...

    Text Solution

    |

  4. Find in parametric form, the equations of the line x+y+z+1=0, 4x+y-2z+...

    Text Solution

    |

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

    Text Solution

    |

  6. Find the equation of the plane containing the line of intersection of ...

    Text Solution

    |

  7. Find the vector quation of the plane containing the line of intersecti...

    Text Solution

    |

  8. Find the equation of the plane which is perpendicular to the plane 5 x...

    Text Solution

    |

  9. Find the equation of the plane bisectiing the angles between the plane...

    Text Solution

    |

  10. Show that the lines (x+4)/3=(y+6)/5=(z-1)/-2 and 3x-2y+z+5=0=2x+3y+4z-...

    Text Solution

    |

  11. Prove that the line of section of the planes 5x+2y-4z+2=0 and 2x+8y+2z...

    Text Solution

    |

  12. Find the equations of the line through the point (1,2,4) and parallel ...

    Text Solution

    |

  13. Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+...

    Text Solution

    |

  14. Prove that the lines x=py+q, z=ry+s and x=p'y+q'z=r'y+s' are at right ...

    Text Solution

    |

  15. Find the equations of the plane through the intersection of the planes...

    Text Solution

    |

  16. Find the equations of the plane which contains the line of intersectio...

    Text Solution

    |

  17. If a line makes angles of 90^@,60^@ and theta with the x, y and z axis...

    Text Solution

    |

  18. Name the locus of the equation x^2+y^2=0.

    Text Solution

    |

  19. What is the locus of the equations x^2+y^2+z^2=0?

    Text Solution

    |

  20. Write the direction cosines of the Y-axis.

    Text Solution

    |