Home
Class 12
MATHS
Find the angle between the planes 2x+y-2...

Find the angle between the planes `2x+y-2x+3=0 and vecr*(6hati+3hatj+2hatk)=5`.

Text Solution

Verified by Experts

Normals along the given planes are `2hati+hatj-2hatk and 6hati+3hatj+2hatk`.
Then angle between planes, `theta = cos^(-1)=((2hati+hatj-2hatk)*(6hati+3hatj+2hatk))/(sqrt((2)^(2)+(1)^(2)+(-2)^(2))sqrt((6)^(2)+(3)^(2)+(2)^(2)))=cos^(-1)""(11)/(12)`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise 3.1|12 Videos
  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise 3.2|15 Videos
  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos
  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the folowing planes :- (i) vecr.(2hati-3hatj+4hatk) = 5 and vecr.(-hati+hatj) = 1 (ii) vecr.(2hati+3hatj-6hatk) = 1 and vecr.(hati-2hatj+2hatk) + 3 = 0 (iii) x+y-2z=3 and 2x-2y+z+1 = 0 (iv) x+y-z=8 and -x+2y+z-1 = 0

Find the acute angle between the following planes: i) vecr.(hati+hatj-2hatk)=5 and vecr.(2hati+2hatj-hatk)=9 ii) vecr.(hati+2hatj-hatk)=6 and vecr.(2hati-hatj-hatk)+3=0

Find the angle between the planes vecr.(hati+hatj)=1 and vecr.(hati+hatk)=3 .

Find the angles between the planes vecr(hati-2hatj-2hatk)=1 and vecr(3hati-6hatj+2hatk)=0

Find the angle between the planes. vecr.(hati+hatj+2hatk)=5 and vecr.(2hati-hatj+hatk)=8 .

The angle between the planes vecr.(2hati-hatj+hatk)=6 and vecr.(hati+hatj+2hatk)=5 is

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

Find the angle between the lines given by vecr=(2hati+3hatj+4hatk)-lambda (hati-4hatj+5hatk) and vecr = (hati-hatj+hatk)-s(2hati-3hatj+4hatk)

Find the angle between the planes vecr.(3hati-4hatj+5hatk)=0 and vecr.(2hati-hatj-2hatk)=7 .

Find the distance between the parallel planes vecr.(2hati-3hatj+6hatk) = 5 and vecr.(6hati-9hatj+18hatk) + 20 = 0 .

CENGAGE-THREE-DIMENSIONAL GEOMETRY -JEE Previous Year
  1. Find the angle between the planes 2x+y-2x+3=0 and vecr*(6hati+3hatj+2h...

    Text Solution

    |

  2. (i) Find the equation of the plane passing through the points(2,1,0...

    Text Solution

    |

  3. Find the equation of a plane passing through (1, 1, 1) and parallel to...

    Text Solution

    |

  4. A parallelepiped S has base points A ,B ,Ca n dD and upper face points...

    Text Solution

    |

  5. Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=...

    Text Solution

    |

  6. A line with positive direction cosines passes through the point P(2, –...

    Text Solution

    |

  7. The value of k such that (x-4)/1=(y-2)/1=(z-k)/2 lies in the plane 2x-...

    Text Solution

    |

  8. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersect...

    Text Solution

    |

  9. A variable plane at distance of 1 unit from the origin cuts the coordi...

    Text Solution

    |

  10. A plane passes through (1,-2,1) and is perpendicualr to two planes 2x...

    Text Solution

    |

  11. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

    Text Solution

    |

  12. Equation of the plane containing the straight line x/2=y/3=z/4 and per...

    Text Solution

    |

  13. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  14. The point P is the intersection of the straight line joining the point...

    Text Solution

    |

  15. Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z...

    Text Solution

    |

  16. Two lines L1x=5, y/(3-alpha)=z/(-2)a n dL2: x=alphay/(-1)=z/(2-alpha) ...

    Text Solution

    |

  17. A line l passing through the origin is perpendicular to the lines l1: ...

    Text Solution

    |

  18. let L be a straight line passing through the origin. Suppose that all ...

    Text Solution

    |

  19. In R^(3), consider the planes P(1):y=0 and P(2),x+z=1. Let P(3) be a p...

    Text Solution

    |

  20. Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parame...

    Text Solution

    |

  21. Consider three planes P(1):x-y+z=1 P(2):x+y-z=-1 and " "P...

    Text Solution

    |