Home
Class 12
MATHS
Show that the normal to the following pl...

Show that the normal to the following planes are perpendicular to each other. ` vec rdot((2 hat i- hat j+3 hat k)=5` & `vec rdot((2 hat i-2 hat j-2 hat k)=5`

Text Solution

Verified by Experts

The equation of the first plane is
`{{r}} \cdot(2 \hat{\i}-\hat{\j}+3 \hat{{k}})=5`
The normal to this plane is `\vec{n}_{1}=2 \hat{i}-\hat{j}+3 \hat{k} \ldots \ldots .({i})`
The equation of the first plane is
...
Promotional Banner

Topper's Solved these Questions

  • TANGENTS AND NORMALS

    RD SHARMA|Exercise Solved Examples And Exercises|244 Videos
  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

Determine the value of lambda for which the following plane are perpendicular to each other. vec rdot(( hat i+2 hat j+3 hat k)=7\ a n d\ vec rdot((lambda hat i+2 hat j-7 hat k)=26.

Show that the following planes are at right angle: vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.

Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=5\ a n d\ vec rdot(( hat i-2 hat j+2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4 .

Find the distance of the point 2 hat i- hat j-4 hat k from the plane vec rdot((3 hat i-4 hat j+12 hat k)-9=0.

For what value of lambda are the vector vec a and vec b perpendicular to each other? where: vec a=lambda hat i+2 hat j+ hat k and vec b=4 hat i-9 hat j+2 hat k vec a=lambda hat i+2 hat j+ hat k and vec b=5 hat i-9 hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k and vec b=3 hat i+2 hat j-lambda hat k vec a=lambda hat i+3 hat j+2 hat k and vec b= hat i- hat j+3 hat k

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

Find a unit vector perpendicular to each one of the vectors vec(a)= ( 4 hat(i) - hat(j)+ 3 hat(k)) and vec(b)=(2hat(i) + 2 hat(j)- hat(k)).

Find the vector and Cartesian equations of the line passing through (1, 2, 3) and parallel to the planes vec rdot(( hat i- hat j+2 hat k)=5\ a n d\ vec rdot((3 hat i+ hat j+ hat k)=6.

RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the equation of the plane that bisects the line segment joining ...

    Text Solution

    |

  2. Show that the normal to the following planes are perpendicular to each...

    Text Solution

    |

  3. Show that the normal to the following planes are perpendicular to each...

    Text Solution

    |

  4. Show that the equation of the planes are perpendicular to each other. ...

    Text Solution

    |

  5. Show that the normal vector to the plane 2x+2y+2z=3 is equally incline...

    Text Solution

    |

  6. Find a vector of magnitude 26 units normal to the plane 12 x-3y+4z=1.

    Text Solution

    |

  7. Find the equation of the plane which bisects the line segment joining ...

    Text Solution

    |

  8. Find the vector and the Cartesian equation of the plane which pases th...

    Text Solution

    |

  9. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

    Text Solution

    |

  10. Find the vector equation of a plane at a distance of 5 units from the ...

    Text Solution

    |

  11. Reduce the equation of the plane x-2y-2z=12 to normal form and hence f...

    Text Solution

    |

  12. Find the vector equation of a plane which is at a distance of 6 units ...

    Text Solution

    |

  13. Find the vector equation of a plane which is at a distance of 3 units ...

    Text Solution

    |

  14. Find the vector equation of a plane which is at a distance of 5 units ...

    Text Solution

    |

  15. Reduce the equation 2x-3y-6z=14 to the normal form and hence fine the ...

    Text Solution

    |

  16. Write the normal form of the equation of the plane 2x-3y+6z+14=0.

    Text Solution

    |

  17. The direction ratios of the perpendicular from the origin to a plane ...

    Text Solution

    |

  18. Find a normal vector to the plane x+2y+3z-6=0

    Text Solution

    |

  19. Find the vector equation of the plane which is at a distance of 6/(sq...

    Text Solution

    |

  20. Find the distance of the plane 2x -3y + 4z-6 = 0from the origin.

    Text Solution

    |