Home
Class 12
MATHS
L1a n dL2 and two lines whose vector equ...

`L_1a n dL_2` and two lines whose vector equations are `L_1: vec r=lambda((costheta+sqrt(3)) hat i+(sqrt(2)sintheta) hat j+(costheta-sqrt(3)) hat k)` `L_2: vec r=mu(a hat i+b hat j+c hat k)` , where `lambdaa n dmu` are scalars and `alpha` is the acute angel between `L_1a n dL_2dot` If the angel `alpha` is independent of `theta,` then the value of `alpha` is a. `pi/6` b. `pi/4` c. `pi/3` d. `pi/2`

A

`(phi)/(6)`

B

`(phi)/(4)`

C

`(phi)/(3)`

D

`(phi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
(a)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

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

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 4|7 Videos

  • THEORY OF EQUATIONS

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

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

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

Similar Questions

Explore conceptually related problems

Find the value of theta(0,pi//2) for which vectors vec a=(sintheta) hat i+(costheta) hat j a n d\ vec b= hat i-sqrt(3) hat j+2 hat k are perpendicular.

Show that the plane whose vector equation is vec r*( hat i+2 hat j= hat k)=3 contains the line whose vector equation is vec r*( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot

Find the shortest distance between the lines l1 and l2 whose vector equations are -> r= hat i+ hat j+lambda(2 hat i- hat j+ hat k) (1)and -> r=2 hat i+ hat j-k+mu(3 hat i-5 hat j+2 hat k) (2)

Find the shortest distance between the following pairs of line whose vector equation are: vec r=( hat i+2 hat j+3 hat k+lambda(2 hat i+3 hat j+4 hat k)a n d\ vec r=(2 hat i+4 hat j+5 hat k)+mu(3 hat i+4 hat j+5 hat k)

Find the shortest distance between the following pairs of line whose vector equation are: vec r=3 hat i+8 hat j+3 hat k+lambda(3 hat i- hat j+ hat k)a n d\ vec r=-3 hat i-7 hat j+6 hat k+mu(-3 hat i+2 hat j+4 hat k)

If theta is an acute angle and the vector (sintheta) hat i+(costheta) hat j is perpendicular to the vector hat i-sqrt(3) hat j ,\ t h e n\ theta= pi/6 b. pi/5 c. pi/4 d. pi/3

Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) are coplanar. Also, find the plane containing these two lines.

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 shortest distance between the lines: vec r= hat i+2 hat j+3 hat k+lambda( hat i-3 hat j+2 hat k)a n d\ vec r=4 hat i+5 hat j+6 hat k+mu(2 hat i+3 hat j+ hat k)dot

ARIHANT MATHS ENGLISH-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Consider the following 3lines in space L1:r=3hat(i)-hat(j)+hat(k)+la...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Let A B C D be a tetrahedron such that the edges A B ,A Ca n dA D ar...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. A parallelopiped is formed by planes drawn through the points (1, 2, 3...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |