Home
Class 12
MATHS
Let L1 be the line r1=2hat(i)+hat(j)-hat...

Let `L_1` be the line `r_1=2hat(i)+hat(j)-hat(k)+lambda(hat(i)+2hat(k))` and let `L_2` be the another line `r_2=3hat(i)+hat(j)+mu(hat(i)+hat(j)-hat(k))`. Let `phi` be the plane which contains the line `L_1` and is parallel to the `L_2`. The distance of the plane` phi` from the origin is

A

`sqrt((2)/(7))`

B

`(1)/(7)`

C

`sqrt(6)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
(a)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

Let L_1 be the line vec r_1=2 hat i+ hat j- hat k+lambda(i+2 hat k) and let L_2 be the line vec r_2=3 hat i+ hat j+mu(i+ hat j- hat k) . Let pi be the plane which contains the line L_1 and is parallel to L_2dot The distance of the plane pi from the origin is a. sqrt(6) b. 1//7 c. sqrt(2//7) d. none of these

The angle between the line r=(hat(i)+2hat(j)-hat(k))+lamda(hat(i)-hat(j)+hat(k)) and the plane r*(2hat(i)-hat(j)+hat(k))=4 is

Show that the lines vec(r ) =(hat(i) -hat(j)) +lambda (2hat(i)+ hat(k)) " and " vec(r ) =(2hat(i) -hat(j)) + mu (hat(i)+ hat(j) -hat(k)) do not intersect .

The acute angle between the line r=(hat(i)+2hat(j)+hat(k))+lamda(hat(i)+hat(j)+hat(k)) and the plane r*(2hat(i)+hat(j)+hat(k))=5

The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-hat(j)+4hat(k)) and the plane rcdot(hat(i)+5hat(j)+hat(k))=5, is

The distance between the line r=2hat(i)-2hat(j)+3hat(k)+lambda(hat(i)-hat(j)+4hat(k)) and the plane rcdot(hat(i)+5hat(j)+hat(k))=5, is

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

Equation of the plane that contains the lines r=(hat(i)+hat(j))+lambda(hat(i)+2hat(j)-hat(k)) and , r=(hat(i)+hat(j))+mu(-hat(i)+hat(j)-2hat(k)) is

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. The position vectors of points a and b are hat(i)-hat(j)+3hat(k) and 3...

    Text Solution

    |

  2. The vector equation of the plane through the point 2hat(i)-hat(j)-4hat...

    Text Solution

    |

  3. Let L1 be the line r1=2hat(i)+hat(j)-hat(k)+lambda(hat(i)+2hat(k)) and...

    Text Solution

    |

  4. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

    Text Solution

    |

  5. The value of m for which straight line 3x-2y+z+3=0=4x-3y+4z+1 is paral...

    Text Solution

    |

  6. The length of projection of the line segmet joining the points (1, 0,...

    Text Solution

    |

  7. The number of planes that are equidistant from four non-coplanar po...

    Text Solution

    |

  8. In a three dimensional co-odinate , P, Q and R are images of a point A...

    Text Solution

    |

  9. A plane passing through (1,1,1) cuts positive direction of coordinates...

    Text Solution

    |

  10. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

    Text Solution

    |

  11. The point of intersecting of the line passing through (0, 0, 1) and in...

    Text Solution

    |

  12. Two system of rectangular axes have the same origin. If a plane cuts t...

    Text Solution

    |

  13. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

    Text Solution

    |

  14. Consider the following 3lines in space L1:r=3hat(i)-hat(j)+hat(k)+la...

    Text Solution

    |

  15. Let r=a+lambdal and r=b+mum br be two lines in space, where a= 5hat(i)...

    Text Solution

    |

  16. L1a n dL2 and two lines whose vector equations are L1: vec r=lambda((c...

    Text Solution

    |

  17. The vector equations of two lines L1 and L2 are respectively vec r=1...

    Text Solution

    |

  18. Consider three vectors p=i+j+k, q=2i+4j-k and r=i+j+3k. If p, q and r ...

    Text Solution

    |

  19. Intercept made by the circle zbarz+bara+a barz+r=0 on the real axis ...

    Text Solution

    |

  20. If the distance between the planes 8x+12y-14z=2 and 4x+6y-7z=2 can be ...

    Text Solution

    |