Home
Class 12
MATHS
The length of the perpendicular drawn...

The length of the perpendicular drawn from `(1,2,3)` to the line `(x-6)/3=(y-7)/2=(z-7)/(-2)` is a. `4` b. `5` c. `6` d. `7`

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
d
Let P be the point (1,2,3) and PN be the length of the perpendicular from P on the given line.
Coordinates of point N are `(3lamda+6,2lamda+7,-2lamda+7)`.
Now PN is perpendicular to the given line of vector
`3veci+2vecj-2veck`. Thus,
`3(3lamda+6-1)+2(2lamda+7-2)-2(-2lamda+7-3)=0orlamda=-1`
Then, point N is (3,5,9)
`impliesPN=7`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Exercise (Reasoning Questions)|10 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE|Exercise SUBJECTIVE TYPE|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

Similar Questions

Explore conceptually related problems

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

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

Find the image of the point (1, 2, 3) in the line (x-6)/(3)=(y-7)/(2)=(z-7)/(-2) .

Find the length and the foot of the perpendicular from the point (7,14 ,5) to the plane 2x+4y-z=2.

The plane which passes through the point (3,2,0) and the line (x-3)/1=(y-6)/5=(z-4)/4 is a. x-y+z=1 b. x+y+z=5 c. x+2y-z=1 d. 2x-y+z=5

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin. a.2x+3y+4z-12=0 b.3y+4z-6=0 c. x+y+z=1 d. 5y+8=0

Find the equation of the plane passing through the line (x-1)/5=(y+2)/6=(z-3)/4 and point (4,3,7)dot

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5

The shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4 is

CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

    Text Solution

    |

  2. Let L be the line of intersection of the planes 2x+3y+z=1a n dx+3y+2z=...

    Text Solution

    |

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

    Text Solution

    |

  4. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

    Text Solution

    |

  5. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=...

    Text Solution

    |

  6. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

    Text Solution

    |

  7. A line makes an angel theta with each of the x-and z-axes. If the a...

    Text Solution

    |

  8. The shortest distance from the plane 12 x+y+3z=327 to the sphere x^...

    Text Solution

    |

  9. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

    Text Solution

    |

  10. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4...

    Text Solution

    |

  11. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

    Text Solution

    |

  12. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

    Text Solution

    |

  13. Two systems of rectangular axes have the same origin. If a plane cu...

    Text Solution

    |

  14. Find the equation of a plane which passes through the point (3, 2, 0...

    Text Solution

    |

  15. The direction ratios of a normal to the plane through (1,0,0)a n d(...

    Text Solution

    |

  16. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

    Text Solution

    |

  17. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

    Text Solution

    |

  18. Distance of the point P(vecc) from the line vecr=veca+lamdavecb is

    Text Solution

    |

  19. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

    Text Solution

    |

  20. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

    Text Solution

    |