Home
Class 12
MATHS
The straight lines, whose direction cosi...

The straight lines, whose direction cosines are `l, m, n` which are the roots of `al+bm+cn=0` and `fl^2+gm^2+hn^2=0` are parallel

A

`f/a + g/b + h/c=0`

B

`a/f + b/g +c/h=0`

C

`f/a^(2) + g/b^(2) + h/c^(2)=0`

D

`a^(2)/f + b^(2)/g +c^(2)/h=0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise PREVIOUS YEAR MHT-CET EXAM QUESTIONS|3 Videos

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP- CHAPTERS 6,7,8|16 Videos

  • PLANE IN SPACE

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP- CHAPTERS 6,7,22|1 Videos

  • PAIR OF STRAIGHT LINES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|19 Videos

  • THREE DIMENSIONAL GEOMETRY

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|39 Videos

Similar Questions

Explore conceptually related problems

A straight line with direction cosines (0,1,0) is

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and ul^(2)+zm^(2)=vm^(2)+wn^(2)=0 are parallel or perpendicular as (a^(2))/(u)+(b^(2))/(v)+(c^(2))/(w)=0 or a^(2)(v+w)+b^(2)(w+u)+c^(2)(u+v)=0

Prove that the straight lines whose direction cosines are given by the relations al+bm+cn=0 and fmn+gnl+hlm=0 are Perpendicular to each other if (f)/(a)+(g)/(b)+(h)/(c)=0 , and parallel if a^(2)f^(2)+b^(2)g^(2)+c^(2)h^(2)-2bcgh-2cahf-2abfg=0 .

The straight lines whose direction cosines are given by al+bm+cn=0 ,fmn+gnl+hlm=0 are perpendicular if

Prove that the two lines whose direction cosines are given by the relations pl+qm+rn=0 and al^2+bm^2+cn^2=0 are perpendicular if p^2(b+c)+q^2(c+a)+r^2(a+b)=0 and parallel if p^2/a+q^2/b+r^2/c=0

The direction cosines of two lines are related by l+m+n=0 and al^(2)+bm^(2)+cn^(2)=0 The linesare parallel if

The angle between the straight lines, whose direction cosines are given by the equations 2l+2m -n=0 and mn+nl+lm=0 , is :

Find the angle between the lines whose direction cosines has the relation l+m+n=0 and 2l^(2)+2m^(2)-n^(2)=0 .

MARVEL PUBLICATION-PLANE IN SPACE -PART B: MASTERING THE BEST ON LINE AND PLANE IN SPACE
  1. Under what condition do the planes bx-ay=n,cy-bz=l,az-cx=m intersect ...

    Text Solution

    |

  2. If the two lines, whose d.C.s l,m,n are given by the equation al+bm+cn...

    Text Solution

    |

  3. The straight lines, whose direction cosines are l, m, n which are the ...

    Text Solution

    |

  4. The perpendicular distance of a corner of uni cube from a diagonal not...

    Text Solution

    |

  5. A line makes an angle alpha, beta, gamma, delta with the four diagonal...

    Text Solution

    |

  6. If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,...

    Text Solution

    |

  7. The shortest distance between the lines x+a=2y=-12z and x=y+2a=6z-6a i...

    Text Solution

    |

  8. The direction Cosines of two lines at right angles are l(1),m(1),n(1)a...

    Text Solution

    |

  9. Two system of rectangular axes have the same origin. If a plane cuts t...

    Text Solution

    |

  10. If h, m1, n1 and l2, m2, n2 are D.C.s of the two lines inclined to eac...

    Text Solution

    |

  11. Let vectors bara, barb, barc and bard be such that (baraxxbarb)xx(ba...

    Text Solution

    |

  12. A non zero vector veca is parallel to the kine of intersection of the ...

    Text Solution

    |

  13. Value of k such that the line (x-4)/1 = (y-2)/1 =(z-k)/2 lies in th...

    Text Solution

    |

  14. IF lines (x-1)/(2) =(y+1)/(3) =(z-1)/(4) and x-3 =(y-k) /(2) = z ...

    Text Solution

    |

  15. If the straighat lines x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=...

    Text Solution

    |

  16. If the straight lines (x-1)/k = (y-2)/2 =(z-3)/3 and (x-2)/3 = (y-3)...

    Text Solution

    |

  17. A variable plane at distance of 1 unit from the origin cuts the coordi...

    Text Solution

    |

  18. If the lines x=ay +b, z=cy+d and x=a'y + b', z=c'y + d' are perpendi...

    Text Solution

    |

  19. The angle between the lines 2x=3y=-z and 6x=-y=-4z is

    Text Solution

    |

  20. A plane which passes through the point (3,2,0), and the line (x-3)/1 =...

    Text Solution

    |