Home
Class 11
MATHS
If (a(1),b(1),c(1)),(a(2),b(2),c(2)) are...

If `(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2))` are direction ratio of two lines such that
`(a_(1)^(2)+b_(1)^(2)+c_(1)^(2))(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))^(2)=0` then the two lines

A

are parallel

B

are perpendicular

C

include an angle `(pi)/(4)`

D

include angle `(pi)/(3)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES & RATIOS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|36 Videos

  • DIRECTION COSINES & RATIOS

    AAKASH SERIES|Exercise EXERCISE - I|4 Videos

  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (PRACTICE SHEET (ADVANCED)) (Integer Type Questions)|5 Videos

  • DIRECTION COSINES AND RATIOS

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|8 Videos

Similar Questions

Explore conceptually related problems

If (a_(1), b_(1), c_(1)), (a_(2), b_(2), c_(2)) are d.r.'s of two perpendicular lines then

If (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) then the lines are………lines.

|(a,b,c),(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2))|=k|(b+c,c+a,a+b),(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2))| then k=

If the lines a_(1)x+b_(1)y=1,a_(2)x+b_(2)y=1,a_(3)x+b_(3)y=1, are concurrent then the points (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))

If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

If |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|=|(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1)| , then the two triangles with vertices (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) and (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3)) must be

AAKASH SERIES-DIRECTION COSINES & RATIOS-EXERCISE - II
  1. A line passes through the points (6,-7,-1) and (2,-3,1). The d.c's of ...

    Text Solution

    |

  2. If the angle between the lines whose direcrtion cosines are (-(2)/(sqr...

    Text Solution

    |

  3. Any point on a line has the coordinates (r+1, r-3, rsqrt(2)+4) where r...

    Text Solution

    |

  4. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are d.c's of two lines then find ...

    Text Solution

    |

  5. If the vertices of a triangle are (1,4,2),(-2,1,2),(2,3,-4) then the a...

    Text Solution

    |

  6. The angle between the lines joining the points (1,1,0), (-3, sqrt(3) +...

    Text Solution

    |

  7. If (a(1),b(1),c(1)),(a(2),b(2),c(2)) are direction ratio of two lines ...

    Text Solution

    |

  8. The angle between any two diagonals of a cube is

    Text Solution

    |

  9. In a unit cube. Find The angle between a diagonal of a cube and the di...

    Text Solution

    |

  10. Angle between a diagonal of a cube with edge of lenth 1 is

    Text Solution

    |

  11. If a line makes angles alpha, beta, lambda,delta with the four diagon...

    Text Solution

    |

  12. If a line makes angles alpha,beta,lambda,delta with the 4 diagonals of...

    Text Solution

    |

  13. If the edges of rectangular parllelopiped are 3,2,1 then the angle bet...

    Text Solution

    |

  14. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are d.c's of two lines whose angl...

    Text Solution

    |

  15. If the d.r.s of the two lines are 1,1,2, -1,2,1 then d.c.s of a line w...

    Text Solution

    |

  16. If the d.r.s of OA, OB are (1,1,-1),(1-2,1) then the d.c.s of the norm...

    Text Solution

    |

  17. If (1,2,1), (1,-3,2) are the direction ratios of two lines and (l, m,n...

    Text Solution

    |

  18. If the d.r's of the lines are 2,1,-2 and 3,-2,6 then the d.r,s of the ...

    Text Solution

    |