Home
Class 12
MATHS
Consider the line L 1 : (x+1)/3=( y-2)...

Consider the line L 1 : `(x+1)/3=( y-2)/1= (z+1)/2`, L 2 : `(x-2)/1=( y+2)/2= (z-3)/3`

A

` 0 `

B

` 17//sqrt 3 `

C

`41//5sqrt3 `

D

`17//5 sqrt 2 `

Text Solution

Verified by Experts

The correct Answer is:
D
The shortest distance between ` L _ 1 and L _ 2 ` is
` (|{:( x _2 - x _ 1 , y _ 2 - y _ 1 , z _ 2- z_ 1 ) , ( a_ 1, b _ 1, c _ 1), ( a_ 2, b _ 2, c _ 2):}| ) /( sqrt ( ( a _ 1 b _ 2 - a _ 2 b _ 1 ) ^ 2 + ( b _ 1 c _ 2 - b _ 2 c _ 1 ) ^ 2 + ( c _ 1 a _ 2 - c _ 2 a _ 1 ) ^ 2 ) ) `
` (|{:( 3,0,4) ,( 3,1,2) ,(1,2,3 ):}| ) / ( sqrt ( 25 + 1 + 49)) = (3 ( 3- 4 ) + 0 + 4 ( 6 - 1) ) / ( sqrt ( 75 )) `
` = ( 17 ) / ( sqrt ( 2 ) ) `
Promotional Banner

Topper's Solved these Questions

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • Linear Programming

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|13 Videos

Similar Questions

Explore conceptually related problems

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The shortest distance between L_(1) and L_(2) is

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The unit vector perpendicular to both L-(1) and L_(2) is

Read the following passage and answer the questions. Consider the lines L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2) L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3) Q. The distance of the point (1, 1, 1) from the plane passing through the point (-1, -2, -1) and whose normal is perpendicular to both the lines L_(1) and L_(2) , is

Read the following passage and answer the questions. Consider the lines L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3) The unit vector perpendicualr to both L_(1) and L_(2) is

Read the following passage and answer the questions. Consider the lines L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3) The distance of the point (1,1,1) from the plane passing throught the point (-1,-2,-1) and whose normal is perpendicular to both the lines L_(1) and L_(2) , is

Consider the line L1=(x+1)/3=(y+2)/1=(z+1)/2 L2=(x-2)/1=(y+2)/2=(z-3)/3 The shortest distance between L_1 and L_2 is

(x+1)/(3)=(y+2)/(1)=(z+1)/(2) and (x-2)/(1)=(y+2)/(2)=(z-3)/(3)

cosider the lines, L1=(x+1)/3=(y+2)/1=(z+2)/2 L2=(x-2)/1=(y+2)/2=(z-3)/3 The distance of the point (1, 1, 1) from the plane passing through the point (-1, -2, -1) and whose normal is perpendicular to both the lines L_1 and L_2 is

The shortest distance between lines L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2) , L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3) is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-LINE-Exercise 2(Miscellaneous Problems)
  1. The length of the perpendicular from P(1,6,3) to the line x/1=(y-1)/(2...

    Text Solution

    |

  2. The equation of a line which passes through the point ( 1, 2...

    Text Solution

    |

  3. P is a point on the line segment joining the points (3, 2, ...

    Text Solution

    |

  4. The equaton of the line in vector and cartesian from that pas...

    Text Solution

    |

  5. Find the vector and the cartesian equations of the lines that passes ...

    Text Solution

    |

  6. The equation of a line 4x-4y-z+11=0=x+2y-z-1 can be put as

    Text Solution

    |

  7. The line (x-2)/3=(y+1)/2=(z-1)/1 intersects the curve x y=c^(I2),z=0 i...

    Text Solution

    |

  8. the lines (x-2)/1 = (y-3)/1 = (z-4)/-k and (x-1)/k = (y-4)/1 = (z-5)/1...

    Text Solution

    |

  9. Find the equation of the perpendicular from point (3,-1,11) to line x...

    Text Solution

    |

  10. The line passing through the points (5,1,a) and (3,b,1) crosses the y...

    Text Solution

    |

  11. If the straight lines (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k=(z-...

    Text Solution

    |

  12. Consider the line L 1 : (x+1)/3=( y-2)/1= (z+1)/2, L 2 : (x-2)/1=(...

    Text Solution

    |

  13. Match the following columns.

    Text Solution

    |

  14. Find the equation of a line passing through (1,-1,0) and parallel to t...

    Text Solution

    |

  15. The direction cosines of the line x-y+2z=5, 3x+y+z=6 are

    Text Solution

    |

  16. The length of the perpendicular drawn from (1,2,3) to the line (x-6)...

    Text Solution

    |

  17. The straight line (x-3)/3=(y-2)/1=(z-1)/0 is Parallel to x-axis Parall...

    Text Solution

    |

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

    Text Solution

    |

  19. If the lines x = 1 + s, y = - 3 - lamda s , z = 1 + la...

    Text Solution

    |

  20. Consider the lines L 1 : ( x - 1 )/ ( 3 ) = ( y + 2 ) / ...

    Text Solution

    |