Home
Class 12
MATHS
Find a unit vector normal to the plane i...

Find a unit vector normal to the plane is `x-2y+2z=6`.

Text Solution

Verified by Experts

The correct Answer is:
`1/3hati-2/3hatj+2/3hatk`
Given equation in vector form is `vecr. (hati-2hatj+2hatk)=6`.
Here, `|hati-2hatj+2hatk|=sqrt(1^(2)+(-2)^(2)+2^(2))=sqrt(9)=3`.
`vecr.(1/3hati-2/3hatj+2/3hatk)=6/3=2`.
Requried unit vector `=(1/3hati-2/3hatj+2/3hatk)`.
Promotional Banner

Topper's Solved these Questions

  • THE PLANE

    RS AGGARWAL|Exercise Exercise 28C|34 Videos

  • THE PLANE

    RS AGGARWAL|Exercise Exercise 28F|18 Videos

  • THE PLANE

    RS AGGARWAL|Exercise Exercise 28A|9 Videos

  • SYSTEM OF LINEAR EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|53 Videos

  • VECTOR AND THEIR PROPERTIES

    RS AGGARWAL|Exercise Exercise 22|24 Videos

Similar Questions

Explore conceptually related problems

Find a unit vector normal to the plane vecr.(2hati-3hatj+6hatk)+14=0 .

Find a unit vector normal to the plane through the points (1, 1, 1), (-1, 2, 3) and (2, -1, 3) .

The unit vector normal to the plane x + 2y +3z-6 =0 is (1)/(sqrt(14)) hati + (2)/(sqrt(14))hatj + (3)/(sqrt(14))hatk.

Find a normal vector to the plane 2x-y+2z=5. Also, find a unit vector normal to the plane.

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

Find the direction cosines of the normal to the plane is (3x-6y+2z=7 .

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

Find the angle between the normal to the planes 2x-y+z=6\ a n d\ x+y+2z=7.

Find the direction ratios of the normal to the plane x+2y-3z=5 .

Find the normal form of the plane x+2y-2z+6=0 . Also find the length of perpendicular from origin to this plane and the d.c.'s of the normal.

RS AGGARWAL-THE PLANE-Exercise 28B
  1. Find the Cartesian equation of the plane whose vector equation is vecr...

    Text Solution

    |

  2. Find the vector equation of a plane whose Cartesian equation is 5x-7y+...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the direction cosines of the normal to the plane is (3x-6y+2z=7.

    Text Solution

    |

  5. For each of the following planes, find the direction cosines of the no...

    Text Solution

    |

  6. Find the vector and Cartesian equations of the plane passing throgh th...

    Text Solution

    |

  7. Find the coordinates of the foot of the perpendicular drawn from the o...

    Text Solution

    |

  8. Find the co-ordinates of the foot of perpendicular and the length of p...

    Text Solution

    |

  9. Find the length of the foot of the perpendicular from the point (1,1,2...

    Text Solution

    |

  10. From the point P(1,2,4) a perpendicular is drawn on the plane 2x+y-2z+...

    Text Solution

    |

  11. Find the coordinates of the foot of the perpendicular and the perpendi...

    Text Solution

    |

  12. Find the coordinates of the image of the point P(1, 3, 4) in the plane...

    Text Solution

    |

  13. Find the point where the line (x-1)/2=(y-2)/-3=(z+3)/4 meets the plane...

    Text Solution

    |

  14. find the coordinates of point where the line through (3,-4,-5) and (2,...

    Text Solution

    |

  15. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

    Text Solution

    |

  16. Find the distance of the point (0,-3,2) from the plane 3x+2y+2z+5=0, ...

    Text Solution

    |

  17. Find the equation of the line passing through the point "P"(4,6,2) ...

    Text Solution

    |

  18. Show that the distance of the point of intersection of the line (x-2)/...

    Text Solution

    |

  19. Find the distance of the point (-1,-5,-10) from the point of the inter...

    Text Solution

    |

  20. Prove tht the normals to the planes 4x+11y+2z+3=0 and 3x-2y+5z=8 are p...

    Text Solution

    |