Home
Class 12
MATHS
Find the length of the perpendicular dra...

Find the length of the perpendicular drawn from the point (5,4,-1) to the line `vec(r)=hat(i)+t(2hat(i)+9hat(j)+5hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt((2109)/(110))` (approx.)
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 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

Find the length of the perpendicular drawn from the point (5,4,-1) to the line vec r= hat i+lambda(2 hat i+9 hat j+5 hat k), wher lambda is a parameter.

Find the equation of the perpendicular drawn from the point P(-1,3,2) to the line vec(r)=(2hat(i)+3hat(k))+t(2hat(i)+hat(j)+3hat(k)) . Also find the coordinates of the foot of the perpendicular from P.

Find the foot of the perpendicular drawn from the point (2hat(i)-hat(j)+5hat(k)) to the line vec(r)=(11hat(i)-2hat(j)-8hat(k))+t(10hat(i)-4hat(j)-11hat(k)) . Find also the length of the perpendicular.

Find the equation of the line passing through the point (2,-1,3) and parallel to the line vec(r)=(hat(i)-2hat(j)+hat(k))+lamda(2hat(i)+3hat(j)-5hat(k))

A line passes through (2,-1,3) and perpendicular to the lines vec(r)=(hat(i)+hat(j)+hat(k))+lamda(2hat(i)-2hat(j)+hat(k)) and vec(r)=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)) . Obtain its vector equation.

Find the vector alpha which is perpendicular to both 4 hat (i) + 5 hat (j) - hat (k) and hat (i) - 4 hat (j) + 5 hat (k) and which satisfies the relation alpha . beta = 21 where beta = 3 hat (i)+ 5 hat (j) - hat (k)

Find the equation of a plane through the intersection of the planes vec(r). (hat(i) + 3hat(j) - hat(k)) =5 and vec(r). (2hat(i) - hat(j) + hat(k)) and passing through the point (2, 1, -2)

Find the shortest distance between the two lines whose vector equations are : vec(r)=(hat(i)+hat(j))+t(2hat(i)-hat(j)+hat(k)), vec(r)=(2hat(i)+hat(j)-hat(k))+s(3hat(i)-5hat(k)+2hat(k))

Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

Find the angle between the following pair of lines vec(r)=(2hat(i)+3hat(j)-5hat(k))+t(hat(i)+2hat(j)-2hat(k))" and"vec(r)=(2hat(i)-6hat(k))+t'(hat(i)+2hat(j)-2hat(k))

CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. Find the distance of the point (1,0,0) from the line (x-1)/(2)=(y+1)/(...

    Text Solution

    |

  2. A(1,0,4), B(0,-11,3), C(2,-3,1) are three points and D is the foot of ...

    Text Solution

    |

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

    Text Solution

    |

  4. Let l(1),m(1),n(1),l(2),m(2),n(2)" and "l(3),m(3),n(3) be the durectio...

    Text Solution

    |

  5. Find the equation of the perpendicular drawn from the point P(-1,3,2) ...

    Text Solution

    |

  6. Find the equation of the line passing through the points A(0,6,-9) and...

    Text Solution

    |

  7. The shortest distance between the lines vec(r)=vec(a)+tvec(b) and vec(...

    Text Solution

    |

  8. The shortest distance between the lines vec(r)=vec(a)(1)+tvec(b)(1) an...

    Text Solution

    |

  9. The condition for intersecting the lines vec(r)=vec(a)(1)+tvec(b)(1) a...

    Text Solution

    |

  10. The condition for collinearity for the two parallel lines vec(r)=vec(a...

    Text Solution

    |

  11. The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(...

    Text Solution

    |

  12. The shortest distance (in units) between the lines vec(r)=(hat(i)+2hat...

    Text Solution

    |

  13. Find the shortest distance between the two lines whose vector equation...

    Text Solution

    |

  14. Find the shortest distance between the two lines whose vector equation...

    Text Solution

    |

  15. Find the shortest distance between the two lines whose vector equation...

    Text Solution

    |

  16. Find the shortest distance distance between the following lines : (x...

    Text Solution

    |

  17. Find the shortest distance distance between the following lines : (x...

    Text Solution

    |

  18. Write the vector equation of the following lines and hence determine t...

    Text Solution

    |

  19. Find the shortest distance between the following pairs of parallel lin...

    Text Solution

    |

  20. Find the shortest distance between the following pairs of parallel lin...

    Text Solution

    |