Home
Class 12
MATHS
Show that the points (hati - hatj + 3 ha...

Show that the points `(hati - hatj + 3 hatk ) and (hati+ hatj + hatk)` are equidistant from the plane `vecr. (5 hati + 2 hatj - 7 hatk ) + 9=0` and lies on opposite side of it.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise LEVEL-1|90 Videos
  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise LEVEL-2|42 Videos
  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos
  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

The line vecr = 2hati - 3 hatj - hatk + lamda ( hati - hatj + 2 hatk ) lies in the plane vecr. (3 hati + hatj - hatk) + 2=0 or not

The angle between the line vecr = ( 5 hati - hatj - 4 hatk ) + lamda ( 2 hati - hatj + hatk) and the plane vec r.( 3 hati - 4 hatj - hatk) + 5=0 is

If the point of intersection of the line vecr = (hati + 2 hatj + 3 hatk ) + lambda( 2 hati + hatj+ 2hatk ) and the plane vecr (2 hati - 6 hatj + 3 hatk) + 5=0 lies on the plane vec r ( hati + 75 hatj + 60 hatk) -alpha =0, then 19 alpha + 17 is equal to :

The position vectors of points A and B are hati - hatj + 3hatk and 3hati + 3hatj - hatk respectively. The equation of a plane is vecr cdot (5hati + 2hatj - 7hatk)= 0 The points A and B

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Find the points of intersection of the line vecr = (2hati - hatj + 2hatk) + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

Show that the point (1,2,1) is equidistant from the planes vecr.(hati+2hatj-2hatk) = 5 and vecr.(2hati-2hatj+hatk) + 3 = 0 .

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

The angle between the planes vecr. (2 hati - 3 hatj + hatk) =1 and vecr. (hati - hatj) =4 is

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

VMC MODULES ENGLISH-THREE DIMENSIONAL GEOMETRY -JEE ADVANCED (ARCHIVE)
  1. Show that the points (hati - hatj + 3 hatk ) and (hati+ hatj + hatk) a...

    Text Solution

    |

  2. Let P be the image of the point (3, 1, 7) with respect to the plane x...

    Text Solution

    |

  3. The equation of the plane passing through the point (1,1,1) and perpen...

    Text Solution

    |

  4. A line with positive direction cosines passes through the point P(2, -...

    Text Solution

    |

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

    Text Solution

    |

  6. A plane which is perpendicular to two planes 2x-2y+z=0 and x-y+2z = 4 ...

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/...

    Text Solution

    |

  9. The equation of the plane containing the line 2x-5y""+""z""=""3;""x...

    Text Solution

    |

  10. The disatance of the point (1, 0, 2) from the point of intersection of...

    Text Solution

    |

  11. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

    Text Solution

    |

  12. The equation of a plane passing through the line of intersection of th...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  15. Equation of the plane containing the straight line (x)/(2)= (y)/(3)= (...

    Text Solution

    |

  16. Consider three planes P(1):x-y+z=1, P(2):x+y-z=-1 and P(3):x-3y+3z=2...

    Text Solution

    |

  17. Consider the planes 3x-6y-2z=15 and 2x+y-2z=5. Statement 1:The parame...

    Text Solution

    |

  18. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

    Text Solution

    |

  19. Two lines L(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L(2) : x=alpha, (y)/(...

    Text Solution

    |

  20. A line l passing through the origin is perpendicular to the lines l(...

    Text Solution

    |

  21. In R(3) , consider the planes P(1):y=0and P(2) : x+z=1. Let P(3) ...

    Text Solution

    |