Home
Class 12
MATHS
Find the angle between the two planes 3...

Find the angle between the two planes `3x - 6y + 2z = 7`and `2x + 2y-2z =5`.

Text Solution

AI Generated Solution

To find the angle between the two planes given by the equations \(3x - 6y + 2z = 7\) and \(2x + 2y - 2z = 5\), we can follow these steps: ### Step 1: Identify the normal vectors of the planes The normal vector of a plane given by the equation \(ax + by + cz = d\) is \(\vec{n} = (a, b, c)\). For the first plane \(3x - 6y + 2z = 7\): - The coefficients are \(a = 3\), \(b = -6\), and \(c = 2\). - Thus, the normal vector \(\vec{n_1} = (3, -6, 2)\). ...
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise Exercise 11.1|5 Videos
  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 11.3|14 Videos
  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|23 Videos
  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 1.3|14 Videos
  • VECTOR ALGEBRA

    NCERT ENGLISH|Exercise Exercise 10.5|7 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the planes 2x - y + 3z = 6 and x + y +2z =7 .

Find the angle between the planes 2x - y + 3z = 6 and x + y +2z =7 .

Find the angle between the two planes 2x + y-2z = 5 and 3x- 6y-2z = 7 using vector method.

Find the angle between the plane: 3x-6y+2z=7 and 2x+2y-2z=5

Find the angle between the plane: 2x-y+z=6 and x+y+2z=7

Find the angle between the planes x-y+2z=9 and 2x+y+z=7 .

Find the angle between the plane: 2x+y-2z=5 and 3x-6y-2z=7

Find the angle between the planes 3x+y+2z=1 and 2x-y+z+3 = 0 .

Find the angle between the planes -x+y+2z=9 and x+2y+z=5

Find the angle between the two lines 2x=3y=-z and 6x=-y=-4z .

NCERT ENGLISH-THREE DIMENSIONAL GEOMETRY-SOLVED EXAMPLES
  1. Find the direction cosines of the line passing through the two points...

    Text Solution

    |

  2. If a line has direction ratios 2,1,2.determine its direction cosines.

    Text Solution

    |

  3. If a line makes angle 90^@, 60^@and 30^@with the positive direction ...

    Text Solution

    |

  4. Find the angle between the pair of lines given by vecr=3 hat i+2 ha...

    Text Solution

    |

  5. The Cartesian equation of a line is (x+3)/2=(y-5)/4=(z+6)/2. Find th...

    Text Solution

    |

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

    Text Solution

    |

  7. Find the vector equation of the plane passing through the intersectio...

    Text Solution

    |

  8. Find the angle between the two planes 3x - 6y + 2z = 7and 2x + 2y-2z ...

    Text Solution

    |

  9. Find the angle between the two planes 2x + y-2z = 5and 3x- 6y-2z = 7...

    Text Solution

    |

  10. Find the distance of a point (2, 5, 3)from the plane vecr.(6 hat i-...

    Text Solution

    |

  11. Find the angle between the pair of lines (x+3)/3=(y-1)/5=(z+3)/4and (x...

    Text Solution

    |

  12. Find the shortest distance between the lines l1 and l2 whose vector ...

    Text Solution

    |

  13. Find the distance between the lines l1and l2given by vec r= hat i+2 ...

    Text Solution

    |

  14. Find the vector equation of the plane which is at a distance of 6/(sqr...

    Text Solution

    |

  15. Find the direction cosines of the unit vector perpendicular to the pla...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Find the vector and cartesian equations of the plane which passes thr...

    Text Solution

    |

  19. Find the vector equations of the plane passing through the points R(2...

    Text Solution

    |

  20. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y...

    Text Solution

    |