Home
Class 12
MATHS
The length of projection of the line ...

The length of projection of the line segment joining the points `(1,0,-1)a n d(-1,2,2)` on the plane `x+3y-5z=6` is equal to a. `2` b. `sqrt((271)/(53))` c. `sqrt((472)/(31))` d. `sqrt((474)/(35))`

A

2

B

`sqrt((271)/(53))`

C

`sqrt((472)/(31))`

D

`sqrt((474)/(35))`

Text Solution

Verified by Experts

The correct Answer is:
d
Let A(1,0,-1), B(-1,2,2) Direction rations of segment AB are `lt2,-2,-3gt`
`becausecostheta=(|2xx1+3(-2)-5(-3)|)/(sqrt(1+9+25)sqrt4+4+9)`
`=(11)/(sqrt17sqrt35)=(11)/sqrt595`
Length of projection `=(AB)sintheta`
`=sqrt((2)^(2)+(2)^(2)+(3)^(2))xxsqrt((474)/(35))` units
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 equation of the plane through the points (2, 3,1)a n d(4,-5,3) and parallel to the x-axis.

The ration in which the line segement joining the points (4,-6) and (3,1) is divided by the parabola y^2=4x is (a) (-20+-sqrt(155))/(11):1 (b) (-20+-sqrt(155))/(11):2 (c) -20+-2sqrt(155): 11 (d) -20+-sqrt(155): 11

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : costheta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))

Equation(s) of the straight line(s), inclined at 30^0 to the x-axis such that the length of its (each of their) line segment(s) between the coordinate axes is 10 units, is (are) (a) x+sqrt(3)y+5sqrt(3)=0 (b) x-sqrt(3)y+5sqrt(3)=0 (c) x+sqrt(3)y-5sqrt(3)=0 (d) x-sqrt(3)y-5sqrt(3)=0

Equation of the pane passing through the points (2,2,1)a n d(9,3,6),a n d_|_ to the plane 2x+6y+6z-1=0 is a. 3x+4y+5z=9 b. 3x+4y-5z=-9 c. 3x+4y-5z=9 d. none of these

Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-2)/1=(y-3)/1=(z-4)/1 is equal to a. sqrt(14) b. sqrt(7) c. sqrt(2) d. none of these

If x=1+1/(3+1/(2+1/(3+1/(2oo)))) a sqrt(5/2) b. sqrt(3/2) c. sqrt(7/3) d. sqrt(5/3)

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

Equation of the pane passing through the points (2,2,1)a n d(9,3,6),a n d_|_ to the plane 2x+6y+6z-1=0 is a. 3x+4y+5z=9 b. 3x+4y-5z=9 c. 3x+4y-5z=9 d. none of these

CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. The coordinates o the foot of the perpendicular drawn from the orig...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. The length of projection of the line segment joining the points (1,...

    Text Solution

    |

  4. The number of planes that are equidistant from four non-coplanar po...

    Text Solution

    |

  5. In a three-dimensional coordinate system, P ,Q ,a n dR are images o...

    Text Solution

    |

  6. A plane passing through (1,1,1) cuts positive direction of coordinates...

    Text Solution

    |

  7. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

    Text Solution

    |

  8. Find the point of intersection of line passing through (0,0,1) and t...

    Text Solution

    |

  9. Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-...

    Text Solution

    |

  10. Distance of point P(vecP) from the plane vecr.vecn=0 is

    Text Solution

    |

  11. The reflection of the point veca in the plane vecr.vecn=q is (A) veca+...

    Text Solution

    |

  12. The angle theta between the line vecr=veca+lambdavecb and the plane ve...

    Text Solution

    |

  13. If a line makes an angel of pi/4 with the positive direction of eac...

    Text Solution

    |

  14. The ratio in which the plane vec rdot( vec i-2 vec j+3 vec k)=17 d...

    Text Solution

    |

  15. then image of the point (-1,3,4) in the plane x-2y=0

    Text Solution

    |

  16. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |