Home
Class 12
MATHS
Show that the lines vec(r)= vec(i)+vec(j...

Show that the lines `vec(r)= vec(i)+vec(j)-vec(k)+lambda(3 vec(i)- vec(j)) and vec(r)= 4 vec(i)-vec(k)+ mu (2 vec(i) +3 vec(k))` intersect. Also find their point of intersection.

Text Solution

Verified by Experts

The correct Answer is:
`4 hat(i)- hat(k) or (4,0,-1)`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic -2 (Long answer type questions-II)|7 Videos

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic - 3 (Very short answer type questions)|13 Videos

  • THREE DIMENSIONAL GEOMETRY

    OSWAAL PUBLICATION|Exercise Topic -2 (Short answer type questions-I)|6 Videos

  • SOLVED PAPER ( Topper Answers March - 2015 )

    OSWAAL PUBLICATION|Exercise PART - E|4 Videos

  • VECTOR ALGEBRA

    OSWAAL PUBLICATION|Exercise Topic - 4 (Short Answer Type Questions - II|7 Videos

Similar Questions

Explore conceptually related problems

If vec(a) = 3vec(i) - 2vec(j) + 2vec(i), vec(b) = 6vec(i) + 4vec(j) - 2vec(k), vec(c ) = 3hat(i) - 2hat(j) - 4hat(k) , Then vec(a).(vec(b) xx vec(c )) is

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

For any vector vec r, (vec r . i)^(2) + (vec r .j)^(2) + (vec r . k )^(2) =

If vec a = 2i-3j and vec b = 2i+3k then, (vec a + vec b). (vec a - vec b)

If vec a = i-j, vec b = i+2k , then vec a . vec b =

If vec a = i+j+k, vec a. vec b = 1 and vec a xx vec b = j-k then vec b =

(vec r . i) (vec r xx i) +(vec r .j) (vec r xx j)+ (vec r . k)(vec r xx k)=

If vec a = i-j+k and vec b = 2i+j-k then |2 vec a - vec b|=

OSWAAL PUBLICATION-THREE DIMENSIONAL GEOMETRY-Topic -2 (Short answer type questions-II)
  1. Find the shortest distance between the lines L(1) " and " L(2) ...

    Text Solution

    |

  2. Find the coordinates of the foot of perpendicular drawn from th poi...

    Text Solution

    |

  3. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

  4. Find the direction cosines of the line (x+2)/2=(2y-7)/6=(5-z)/6dot Als...

    Text Solution

    |

  5. Find the shortest distance between two lines whose vector equations ar...

    Text Solution

    |

  6. Show that the lines (x+1)/(3)=(y+3)/(5) =(z+5)/(7) " and " (x-2)/(1...

    Text Solution

    |

  7. Show that the lines (5-x)/-4=(y-7)/4=(z+3)/-5 and (x-8)/7=(2y-8)/2=(z-...

    Text Solution

    |

  8. Show that the lines vec(r)= vec(i)+vec(j)-vec(k)+lambda(3 vec(i)- vec(...

    Text Solution

    |

  9. The equation of line passing through (3,-1,2) and perpendicular to the...

    Text Solution

    |

  10. Find the equation of the line passing through the point (2, 1, 3) and ...

    Text Solution

    |

  11. Find the values of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2an...

    Text Solution

    |

  12. Find the shortest distance between the lines whose vector equations ar...

    Text Solution

    |

  13. Find the equation of the perpendicular drawn from the point (2,4,-1) t...

    Text Solution

    |

  14. Using vectors show that the points A(-2,3,5),B(7,0,-1)C(-3,-2,-5) and ...

    Text Solution

    |

  15. Show that the lines vec(r ) =(hat(i) -hat(j)) +lambda (2hat(i)+ ha...

    Text Solution

    |

  16. Find the Vector and Cartesian equations of the line passing through...

    Text Solution

    |

  17. Find the shortest distance between the following pair of lines : (...

    Text Solution

    |

  18. 2/ Find the perpendicular distance of the point (1, 0, 0) from the lin...

    Text Solution

    |

  19. Find the shortest distance between the following lines whose vector...

    Text Solution

    |

  20. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

    Text Solution

    |