Home
Class 12
MATHS
Find the direction cosines of perpendicu...

Find the direction cosines of perpendicular from the origin to the plane ` vec rdot(2 hat i-3 hat j-6 hat k)+5=0.`

Text Solution

Verified by Experts

` vec rdot(2 hat i-3 hat j-6 hat k)+5=0.`
`=>r((-2 hat i+3 hatj+6 hat k)=5 `
`|r|=sqrt(2^2+3^2+6^2)=7`
So,
directional cosines are, `(-2/7,3/7,6/7)`
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

Find the direction cosines of the unit vector perpendicular to the plane vec rdot((6 hat i-3 hat j-2 hat k)+1=0 passing through the origin.

Find the length and the foot of the perpendicular from the point (1, 1, 2) to the plane vec rdot(( hat i-2 hat j+4 hat k)+5=0.

Write the plane vec rdot((2 hat i+3 hat j-6 hat k)=14 in normal form.

Find the direction cosines of the unit vector perpendicular to the plane quad vec r*(6hat i-3hat j-2hat k)+1=0 passing through the origin.

Find the direction cosines of the unit vector prpendicular to the plane vec r*(6hat i-3hat j-2hat k)+1=0 passing through the origin.

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

Find the equation of the plane through the line of intersection of the planes vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0, which is at a unit distance from the origin.

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.

Find the unit vectors perpendicular to the plane of the vectors vec(a) = 2 hat(i) - 6 hat(j)- 3 hat(k) and vec(b)= 4 hat(i) + 3 hat(j) - hat(k).

RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Reduce the equation vec rdot(3 hat i-4 hat j+12 hat k)=5 to normal fo...

    Text Solution

    |

  2. Find the vector equation of a plane which is at a distance of 8 units ...

    Text Solution

    |

  3. Find the direction cosines of perpendicular from the origin to the ...

    Text Solution

    |

  4. Find the coordinates of the foot of the perpendicular drawn from the ...

    Text Solution

    |

  5. Find the equation of a plane which is at a distance of 3sqrt(3) units ...

    Text Solution

    |

  6. Find the equation of the plane passing through the point (-1,2,1) and ...

    Text Solution

    |

  7. Find the vector equation of the plane passing through the points A(2,2...

    Text Solution

    |

  8. Find the equation of the plane passing through the point (1,2,1) and p...

    Text Solution

    |

  9. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

    Text Solution

    |

  10. Find the vector equation of the plane passing through the points havin...

    Text Solution

    |

  11. Find the equation of the plane through the points P(1,\ 1,\ 0),\ Q(1,\...

    Text Solution

    |

  12. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  13. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  14. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  15. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  16. Find the equation of the plane passing through the following points: (...

    Text Solution

    |

  17. Show that the following points are coplanar: (0,\ -1,\ 0),\ (2,\ 1,\ -...

    Text Solution

    |

  18. Show that the following points are coplanar: (0,\ 4,\ 3),\ (-1,\ -5,\ ...

    Text Solution

    |

  19. Show that the point (0, -1, -1), (4 5, 1), (3, 9, 4) and (-4, 4, 4) ar...

    Text Solution

    |

  20. Reduce the equation of the plane 2x+3y-z=6 to intercept form and find ...

    Text Solution

    |