Home
Class 12
MATHS
The vector equations of two lines L1 an...

The vector equations of two lines `L_1 and L_2` are respectively `vec r=17hat i–9hat j+9hat k+ lambda(3hat i +hat j+ 5hat k) and vec r=15hat –8hat j-hat k+mu(4hat i+3hat j)` `I` `L_1 and L_2` are skew lines `II` `(11, -11, -1)` is the point of intersection of `L_1 and L_2` `III` `(-11, 11, 1)` is the point of intersection of `L_1 and L_2`. `IV ` `cos^-1 (3/sqrt35)` is the acute angle between `_1 and L_2` then , Which of the following is true?

A

`(-11,11,1)` is the point of intersection of `L_(1)` and `L_(2)`

B

`(11,-11,-1)` is the point of intersection of `L_(1)` and `L_(2)`

C

`L_(1)` and `L_(2)` are skew lines

D

`cos^(-1)(3/(sqrt(35)))` is the acute angle between `L_(1)` and `L_(2)`

Text Solution

Verified by Experts

NA
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise MATHEMATICS|259 Videos

Similar Questions

Explore conceptually related problems

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=(2 hat i- hat j- hat k)+mu(2 hat i+ hat j+2 hat k)

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=2 hat i- hat j- hat k+mu(2 hat i+ hat j+2 hat k)

Find the distance between the lines l_1 and l_2 given by vec r= hat i+2 hat j-4k+lambda(2 hat i+3 hat j+6 hat k) and vec r=3 hat i+3 hat j-5k+mu(2 hat i+3 hat j+6 hat k) .

Find the distance between the lines l_1a n d\ l_2 given by vec r= hat i+2 hat j-4 hat k+lambda(2 hat i+3 hat j+6 hat k)a n d\ ,\ vec r=3 hat i+3 hat j-5 hat k+mu(2 hat i+3 hat j+6 hat k)dot

Find the shortest distance between the lines -> r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and -> r=2 hat i- hat j- hat k+mu(2 hat i+ hat j+2 hat k)

Find the shortest distance between lines -> r=6 hat i+2 hat j+ hat k+lambda( hat i-2 hat j+2 hat k) and -> r=-4 hat i- hat k+mu(3 hat i-2 hat j-2 hat k) .

Find the angle between the line vec r = (2 hat i-hat j +3 hat k)+ lambda (3 hat i-hat j+2 hat k ) and the plane vec r.(hat i + hat j + hat k)=3

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Determine whether the following pair of lines intersect or not. vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

Determine the shortest distance between the pair of lines : vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d\ vec r=(2 hat i- hat k)+mu(2 hat i+2 hat k)dot

RESONANCE ENGLISH-TEST SERIES-MATHEMATICS
  1. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  2. a, b ,c are three unit of vectors, a and b are perpendicular to each o...

    Text Solution

    |

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

    Text Solution

    |

  4. If r=hat(i)+hat(j)+lambda(2hat(i)+hat(j)+4hat(k)) and r*(hat(i)+2hat(j...

    Text Solution

    |

  5. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  6. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  7. A multiple choice question has n options, of whlch only one is correct...

    Text Solution

    |

  8. A multiple choice question has n options, of whlch only one is correct...

    Text Solution

    |

  9. Find the equation of the plane passing through A(2,2,-1),B(3,4, 2) ...

    Text Solution

    |

  10. A plane P(1) passing through A(1,2,3), B(3,1,5) and C(-1,0,1) is rotat...

    Text Solution

    |

  11. A line makes angles angle, beta, gamma and delta with the diagonals of...

    Text Solution

    |

  12. The plane x-y-z=2 is rotated through 90^(@) about its line of intersec...

    Text Solution

    |

  13. The volme of a tetrahedron having vertices A(1,1,1),B(1,2,4),C(3,1,-2)...

    Text Solution

    |

  14. The number of integral values of a in [0,10) so that function, f(x)=x^...

    Text Solution

    |

  15. A boy has 3 library tickets and 8 books of his interest in the library...

    Text Solution

    |

  16. The center of the ellipse (x+y-2)^(2)/9+(x-y)^(2)/16=1is

    Text Solution

    |

  17. An isosceles triangle that can be inscribed in an ellipse (x^(2))/(a^(...

    Text Solution

    |

  18. If the range of the function y=(x-1)/(x+1) on the interval 0lexle4 be ...

    Text Solution

    |

  19. Two smallest squares are chose at random on a chess board and p/q is t...

    Text Solution

    |

  20. There are four bags. The first bag contains 10 identical red balls, th...

    Text Solution

    |