Home
Class 12
MATHS
Distance of the point P(x2, y2, z2) from...

Distance of the point `P(x_2, y_2, z_2)` from the line `(x-x_1)/l=(y-y_1)/m=(z-z_1)/n`, where `l,m,n` are the direction cosines of the line, is

A

`sqrt((x_(2)-x_(1))l+ (y_(2)-y_(1))m + (z_(2)-z_(1))n)`

B

`sqrt((x_(2)-x_(1))^(2)l + (y_(2)-y_(1))^(2)m + (z_(2)-z_(1))^(2)n)`

C

`sqrt((x_(2)-x_(1))^(2) + (y_(2)-y_(1))^(2) + (z_(2)-z_(1))^(2))`

D

`sqrt((x_(1)-x_(2))^(2) + (y_(1)-y_(2))^(2) + (z_(1)-z_(2))^(2) -l(x_(1)-x_(2)) + m(y_(1)-y_(2)) + n(z_(1)-z_(2))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|582 Videos

  • LINEAR PROGRAMMING

    NIKITA PUBLICATION|Exercise MCQs|101 Videos

Similar Questions

Explore conceptually related problems

The direction cosines of the line x-y+2z=5,3x+y+z=6 are

The condition that the line (x-x_(1))/(l)=(y-y_(1))/(m)=(z-z_(1))/(n) lies in the plane ax+by+cz+d=0 is

Points (1,-1,2) is the foot of perpendicular drawn from point (0,3,1) on the line (x-a)/l=(y-2)/3=(z-b)/4 find the shortest distance between this line and the line (x-1)/3=(y-2)/4=(z-3)/5

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3. What are the direction ratios of the line of intersection of the given planes?

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3 . What are the direction ratios of the line of intersection of the given planes

Find the equation of the plane through the line (x-x_1)/l_1=(y-y_1)/m_1=(z-z_1)/n_1 and parallel to the line (x-alpha)/l_2=(y-beta)/m_2=(z-gamma)/n_2

Find the acute angle between the lines (x-1)/(l)=(y+1)/(m)=(1)/(n) and =(x+1)/(m)=(y-3)/(n)=(z-1)/(l) where l>m>n, and l,m,n are the roots of the cubic equation x^(3)+x^(2)-4x=4

Acute angle between the lines (x-1)/(l)=(y+1)/(m)=(z)/(n) and (x+1)/(m)=(y-3)/(n)=(z-1)/(l) where l>m>n and l,m,n are the roots of the cubic equation x^(3)+x^(2)-4x=4 is equal to: cos^(-1)(4)/(9)(b)sin^(-1)(sqrt(65))/(9)2cos^(-1)sqrt((13)/(18))(d)cot^(-1)(4)/(65)

NIKITA PUBLICATION-LINE-MULTIPLE CHOICE QUESTIONS
  1. The position vector of the foot of the perpendicular draw from the poi...

    Text Solution

    |

  2. Find the length of the perpendicular drawn from the point (5, 4, -1) t...

    Text Solution

    |

  3. Find the shortest distance between the following lines : (i) vecr=4h...

    Text Solution

    |

  4. Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+l...

    Text Solution

    |

  5. The shortest distance between the lines vecr = (2hati - hatj) + lambda...

    Text Solution

    |

  6. The shortest distance between the lines vecr = (-hati - hatj) + lambd...

    Text Solution

    |

  7. Find the shortest distance between the lines ( x + 1 ...

    Text Solution

    |

  8. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/...

    Text Solution

    |

  9. The shortest distance between the lines (x-5)/4 = (y-7)/-5 = (z+3)/-5 ...

    Text Solution

    |

  10. If OA=a, OB=b, OC=c are the co-terminus edges of regular parallelopipe...

    Text Solution

    |

  11. If OA=a, OB=b, OC=c are the co-terminus edges of regular parallelopip...

    Text Solution

    |

  12. Prove that the shortest distance between the diagonals of a rectangula...

    Text Solution

    |

  13. The line vecr = (8vec - 9vecb + 10vecc) + lambda(3veca - 16vecb + 7vec...

    Text Solution

    |

  14. The lines given by vecr = (hati - hatj) +lambda(2hati +hatk) and vecr ...

    Text Solution

    |

  15. The lines x/1=y/2=z/3 and (x-1)/(-2)=(y-2)/(-4)=(z-3)/(-6) are

    Text Solution

    |

  16. If a,b,c and 1/(bc), 1/(ca), 1/(ab) are the direction ratio of two lin...

    Text Solution

    |

  17. The lines (x-1)/2= (y-2)/4 = (z-3)/6 and (x-1)/4 = (y-2)/5 = (z-3)/7 a...

    Text Solution

    |

  18. Distance of the point P(x2, y2, z2) from the line (x-x1)/l=(y-y1)/m=(z...

    Text Solution

    |

  19. The equation of line equally inclined to coordinate axes and passing t...

    Text Solution

    |

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

    Text Solution

    |