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

II abd IV

B

I and IV

C

Only IV

D

III and IV

Text Solution

Verified by Experts

The correct Answer is:
(b)
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

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is

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

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

Consider the equation of the straight lines given by L_(1):vec r=hat i+hat j+lambda(2hat i-hat j+hat k) and L_(2):vec r=2hat i+hat j-hat k+mu(4hat i-2hat j-2hat k)

Shortest distance between the lines: vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+u(2hat i+4hat j-5hat k)

Find the shortest distance between the lines vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Find the distance between the lines l_(1) and given by quad vec r=hat i+2hat j-4k+lambda(2hat i+3hat j+6hat k) and quad vec r=3hat i+3hat j-5k+mu(2hat i+3hat j+6hat k)

The shortest distance between the line L_1=(hat i - hat j hat k) lambda (2 hat i - 14 hat j 5 hat k) and L_2=(hat j hat k) mu (-2 hat i - 4 hat 7 hat) then L_1 and L_2 is

Equation of the plane containing the lines vec r=(hat i-2hat j+hat k)+t(hat i+2hat j-hat k)vec r=(hat i+2hat j-hat k)+s(hat i+hat j+3hat k) is

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Let r=a+lambdal and r=b+mum br be two lines in space, where a= 5hat(i)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. A plane passes through thee points P(4, 0, 0) and Q(0, 0, 4) and is pa...

    Text Solution

    |

  8. If from the point P(f, g, h) perpendicular PL and PM be drawn to yz an...

    Text Solution

    |

  9. The plane XOZ divides the join of (1, -1, 5) and (2, 3, 4)in the ratio...

    Text Solution

    |

  10. A variable plane forms a tetrahedron of constant volume 64k^3 with the...

    Text Solution

    |

  11. Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutual...

    Text Solution

    |

  12. Equations of the line which passe through the point with position vect...

    Text Solution

    |

  13. Which of the following planes are parallel but not identical? P1: 4x...

    Text Solution

    |

  14. A parallelopied is formed by planes drawn through the points (1, 2, 3)...

    Text Solution

    |

  15. Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(...

    Text Solution

    |

  16. The vector equations of two lines L1 and L2 are respectively, L1:r=2i+...

    Text Solution

    |

  17. Consider the plane (x,y,z)= (0,1,1) + lamda(1,-1,1)+mu(2,-1,0) The dis...

    Text Solution

    |

  18. The value of a for which the lines (x-2)/(1)=(y-9)/(2)=(z-13)/(3) and ...

    Text Solution

    |

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

    Text Solution

    |

  20. Given planes P1:cy+bz=x P2:az+cx=y P3:bx+ay=z P1, P2 and P3 pass...

    Text Solution

    |