Home
Class 12
MATHS
Find the coordinates of the foot of t...

Find the coordinates of the foot of the perpendicular drawn from point `A(1,0,3)` to the join of points `B(4,7,1)a n d C(3,5,3)dot`

Text Solution

Verified by Experts

Let D be the foot of the perpendicular and let is divide BC in the ratio `lamda:1` . Then the coordinates of D are `(3lamda+4)/(lamda+1),(5lamda+7)/(lamda+1)and(3lamda+1)/(lamda+1)`.
Now, `" "vec(AD)botvec(BC)rArrvec(AD)*vec(BC)=0`
`rArr" "(2lamda+3)+2(5lamda+7)+4=0`
`or" "lamda=-(7)/(4)`
Thus, coordinates of D are `(5)/(3), (7)/(3) and (17)/(3)`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Find the coordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1.

Find the coordinates of the foot of perpendicular from the point (-1, 3) to the line 3x - 4y - 16 = 0 .

The foot of the perpendicular drawn from the point (1,8,4) on the line joining the points (0,-11,4) and (2,-3,1) is

The coordinates of the foot of the perpendicular from the point (2,3) on the line -y+3x+4=0 are given by

The coordinates of the foot of the perpendicular drawn from the point P(1, 2, 1) to the straight line joining the points Q(1, 4, 6) and R(5, 4, 4) are -

The coordinates of the foot of the perpendicular drawn from the origin to the line joining the point (-9,4,5)a n d(10 ,0,-1) will be a. (-3,2,1) b. (1,2,2) c. (4,5,3) d. none of these

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

Find the foot of perpendicular drawn from the point (2, 2) to the line 3x - 4y + 5 = 0

The coordinates of the foot of the perpendicular drawn from the point A(2, 4, -1) on the line (x+5)/(1)=(y+3)/(4)=(z-6)/(-9) are -

Find the length of the perpendicular drawn from point (2,3,4) to line (4-x)/2=y/6=(1-z)/3dot

CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the acute angle between the lines (x-1)/l=(y+1)/m=1/na n d=(x+...

    Text Solution

    |

  2. Find the length of the perpendicular drawn from point (2,3,4) to li...

    Text Solution

    |

  3. Find the coordinates of the foot of the perpendicular drawn from po...

    Text Solution

    |

  4. Find the vector equation of the line passing through (1,2,3) and par...

    Text Solution

    |

  5. The value of m for which the straight line 3x-2y+z+3 = 0=4x-3y+4z+1. i...

    Text Solution

    |

  6. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alph...

    Text Solution

    |

  7. Find the equation of line x+y-z-3=0=2x+3y+z+4 in symmetric form. Find ...

    Text Solution

    |

  8. Find the vector equation of line passing through the point (1,2,-4)...

    Text Solution

    |

  9. Find the vector equation of line passing through A(3,4-7)a n dB(1,-...

    Text Solution

    |

  10. Find Cartesian and vector equation of the line which passes through...

    Text Solution

    |

  11. Find the equation of a line which passes through the point (2,3,4) ...

    Text Solution

    |

  12. Find the points where line (x-1)/2=(y+2)/(-1)=z/1 intersects x y ,y za...

    Text Solution

    |

  13. A mirror and source of light are situated at the origin O and a point ...

    Text Solution

    |

  14. The Cartesian equation of a line is (x-3)/2=(y+1)/(-2)=(z-3)/5 . Fi...

    Text Solution

    |

  15. The Cartesian equations of a line are 6x-2=3y+1=2z-2. Find its dire...

    Text Solution

    |

  16. A line passes through the point with position vector 2 hat i-3 hat ...

    Text Solution

    |

  17. Find the plane of the intersection of x^2+y^2+z^2+2x+2y+2=0 and 4x^2...

    Text Solution

    |

  18. Let l1a n dl2 be the two skew lines. If P ,Q are two distinct points o...

    Text Solution

    |

  19. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/1=(...

    Text Solution

    |

  20. Find the angle between the lines 2x=3y=-z and 6x=-y=-4z

    Text Solution

    |