Home
Class 12
MATHS
If vecr=(hati+2hatj+3hatk)+lambda(hati-h...

If `vecr=(hati+2hatj+3hatk)+lambda(hati-hatj+hatk)` and `vecr=(hati+2hatj+3hatk)+mu(hati+hatj-hatk)` are two lines, then the equation of acute angle bisector of two lines is

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

If vecr=(hati+2hatj+3hatk)+lamda(hati-hatj+hatk) and vecr=(hati+2hatj+3hatk)+mu(hati+hatj-hatk) are two lines, then find the equation of acute angle bisector of two lines.

Show that the lines vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk) and vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk) are coplanar. Also the find the equation of the plane passing through these lines.

The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati+phatj+phatk) are perpendicular it p=

Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr= 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk) .

The equation of plane which passes through the point of intersection of lines vecr=hati+2hatj+3hatk+lamda(3hati+hatj+2hatk) and vecr=3hati+hatj+2hatk+mu(hati+2hatj+3hatk) where lamda,muinR and has the greastest distance from the origin is :

Show that the line vecr = (hati+hatj-hatk)+lambda(3hati-hatj) vecr = (4hati-hatk)+mu(2hati+3hatk) are coplanar. Also find the equation of plane in which these lines lie.

If vecr = hati + hatj + lamda( 2 hati + hatj + 4 hatk ) and vecr (hati + 2 hatj - hatk)=3 are the equations of a line and a plane respectively then which of the following is true ?

The line whose vector equation are vecr =2 hati - 3 hatj + 7 hatk + lamda (2 hati + p hatj + 5 hatk) and vecr = hati - 2 hatj + 3 hatk+ mu (3 hati - p hatj + p hatk) are perpendicular for all values of gamma and mu if p equals :

If d is the shortest distance between the lines vecr =(3hati +5hatj + 7hatk)+lambda (hati +2hatj +hatk) and vecr = (-hati -hatj-hatk)+mu(7hati-6hatj+hatk) then 125d^(2) is equal to ____________.

Statement 1 : Lines vecr= hati-hatj+ lamda (hati+hatj-hatk) and vecr= 2hati-hatj+ mu (hati+hatj-hatk) do not intersect. Statement 2 : Skew lines never intersect.

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the equation of the plane passing through the straight line (x...

    Text Solution

    |

  2. Find the equation of the line drawn through the point (1, 0,2) to meet...

    Text Solution

    |

  3. If vecr=(hati+2hatj+3hatk)+lambda(hati-hatj+hatk) and vecr=(hati+2hatj...

    Text Solution

    |

  4. Find the coordinates of a point on the (x-1)/2=(y+1)/(-3)=z atg a d...

    Text Solution

    |

  5. Line L1 is parallel to vector vecalpha=-3 hat i+2 hat j+4 hat k and p...

    Text Solution

    |

  6. Find the values p so that line (1-x)/3=(7y-14)/(2p)=(z-3)/2a n d(7-7x)...

    Text Solution

    |

  7. Find the angel between the following pair of lines: vec r=2 hat i...

    Text Solution

    |

  8. Fid the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime)...

    Text Solution

    |

  9. Find the acute angle between the lines (x-1)/l=(y+1)/m=1/na n d=(x+...

    Text Solution

    |

  10. Find the length of the perpendicular drawn from point (2,3,4) to li...

    Text Solution

    |

  11. Find the coordinates of the foot of the perpendicular drawn from po...

    Text Solution

    |

  12. Find the vector equation of the line passing through (1,2,3) and pa...

    Text Solution

    |

  13. Find the value of m for which thestraight line 3x-2y+z+3=0=4x+3y+4z+1...

    Text Solution

    |

  14. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alph...

    Text Solution

    |

  15. Find the equation of line x+y-z-3=0=2x+3y+z+4 in symmetric form. Find ...

    Text Solution

    |

  16. Find the vector equation of line passing through the point (1,2,-4)...

    Text Solution

    |

  17. Find the vector equation of line passing through A(3,4-7)a n dB(1,-...

    Text Solution

    |

  18. Find Cartesian and vector equation of the line which passes through...

    Text Solution

    |

  19. Find the equation of a line which passes through the point (2,3,4) ...

    Text Solution

    |

  20. Find the points where line (x-1)/2=(y+2)/(-1)=z/1 intersects x y ,y za...

    Text Solution

    |