Home
Class 12
MATHS
Show that the pair of lines whose direct...

Show that the pair of lines whose direction cosines are given by `3lm-4ln+mn=0` and `l+2m+3n=0` are perpendicular to each other.

Text Solution

Verified by Experts

The correct Answer is:
Therefore the given lines are perpendicular to each other
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Exercise 4A|81 Videos

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 Videos

  • SIGNIFICANCE OF DERIVATIVE AS RATE OF CHANGE

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITVE EXAMINATION|20 Videos

  • TANGENT AND NORMAL

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Show that the pair of lines whose direction cosines are given by 3 lm-4ln+mn =0 and l+2m+3n = 0 are perpendicular to each other.

Show that the pair of staright lines whose direction cosines are given by al+bm+cn=0 and pl^(2)+qm^(2)+rn^(2)=0 are perpendicular to each other if a^(2)(q+r)+b^(2)(r+p)+c^(2)(p+q) =0

Find the angle between the line whose direction cosines are given by l+m+n=0a n dl^2+m^2-n^2=0.

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and u l^2+v m^2+w n^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

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2=0.

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

Prove that the straight lines whose direction cosines are given by a^(2)l+b^(2)m+c^(2)n=0 and mn+nl+lm=0 are parallel if a+b+c=0 .

The pair of lines whose direction cosines are given by the equations 3l+m+5n=0a n d6m n-2n l+5l m=0 are a. parallel b. perpendicular c. inclined at cos^(-1)(1/6) d. none of these

Find the angle between the two straight lines whose direction cosines are given by 2l+2m-n=0, mn+nl+lm=0

Prove that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and fmn+gnl+hlm=0 are at right angles if f/a+g/b+h/c=0

CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Sample Questions for Competitive Examination
  1. Show that the pair of lines whose direction cosines are given by 3lm-4...

    Text Solution

    |

  2. The symmetrical from of the lines x+y+z-1=0 and 4x+y-2z+2=0 are -

    Text Solution

    |

  3. The equation of line passing through the point vec(a) parallel to the ...

    Text Solution

    |

  4. The lines vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j)) and vec(r)...

    Text Solution

    |

  5. Consider the lines (x-5)/(3)=(y-7)/(-16)=(z-3)/(7) and (x-9)/(3)=(y-13...

    Text Solution

    |

  6. The distance of the point A(veca) from the line vec(r)=vec(b)+tvec(c)...

    Text Solution

    |

  7. If the length of the perpendicular drawn from (1,2,3) to the line (x-6...

    Text Solution

    |

  8. If the shortest distance between the lines (x-1)/(1)=(y-1)/(1)=(z-1)/(...

    Text Solution

    |

  9. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy xy=c^(...

    Text Solution

    |

  10. A line passing through the point (1,1,1) from a tiangle of area sqrt(6...

    Text Solution

    |

  11. The direction cosines of two lines satisfy the relations lamda(l+m)=n ...

    Text Solution

    |

  12. Each question in this section contains statements given in two columns...

    Text Solution

    |

  13. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

    Text Solution

    |

  14. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

    Text Solution

    |

  15. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

    Text Solution

    |

  16. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

    Text Solution

    |

  17. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

    Text Solution

    |

  18. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

    Text Solution

    |

  19. Statement - I: The point A (1,0,7) is the mirror image of the point B(...

    Text Solution

    |

  20. Statement - I : The lines vec(r)=hat(i)+hat(j)-hat(k)+S(3hat(i)-hat(j)...

    Text Solution

    |