Home
Class 12
MATHS
The distance between two points P and Q ...

The distance between two points P and Q is d and the length of their projections of PQ on the co-ordinate planes are `d _(1),d_(2), d_(3).` Then `d _(1) ^(2) + d_(2)^(2) + d_(3) ^(2) = kd ^(2),` where k is `"_____."`

A

1

B

5

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

  • THREE DIMENSIONAL GEOMETRY

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

  • STRAIGHT LINES AND PAIR OF STRAIGHT LINES

    DISHA PUBLICATION|Exercise EXERCISE 2: CONCEPT APPLICATOR|30 Videos

  • TRIGONOMETRIC FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE-2|30 Videos

Similar Questions

Explore conceptually related problems

The distance between two points P and Q is d and the lengths of projections of PQ on the coordinate planes are l_(1),l_(2),l_(3) then (l_(1)+l_(2)^(2)+l_(3)^(2))/(d^(2)

A(1,1) and B(2,-3) are two points and D is a point on AB produced such that AD=3AB Find the co-ordinates of D.

The length of the diagonal of a square is d units.The area of the square is d^(2)( b) (1)/(2)d^(2)(1)/(4)d^(2)(d)2d^(2)

If the distance between the points P(a cos48^(@),0) and Q(0,a cos12^(@)) is d, then d^(2)-a^(2)=

If the distance between the points (a cos48^(0),0) and (0,a cos12^(@)) is d , then d^(2)-a^(2)=

If the length of perpendicular from the point (-1,2,-2) on the line (x+1)/(2)=(y-2)/(-3)=(z+2)/(4) is d then d^(2)

If d_(1) , d_(2) ( d_(1) > d_(2) ) denote the lengths of the perpendiculars from the point (2,3) on the lines given by 15x^(2)+31xy+14y^(2)=0 , then d_(1)^(2) - d_(2)^(2) + (1)/(74) + (1)/(13) is equal to

DISHA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Exercise -1 : Concept Builder (Topicwise)
  1. Three lines with direction ratios lt 1, 1,2 gtlt sqrt3-1 , -sqrt3-1,...

    Text Solution

    |

  2. What is the sum of the squares of direction cosines of the line joinin...

    Text Solution

    |

  3. The distance between two points P and Q is d and the length of their p...

    Text Solution

    |

  4. The projections of a directed line segment on the coordinate axes are ...

    Text Solution

    |

  5. The projections of the segment PQ on the coordinate axes are -9,12,-8 ...

    Text Solution

    |

  6. L1a n dL2 and two lines whose vector equations are L1: vec r=lambda((c...

    Text Solution

    |

  7. If vecr=(hati+2hatj+3hatk)+lamda(hati-hatj+hatk) and vecr=(hati+2hatj+...

    Text Solution

    |

  8. The lines (x-20/1=(y-3)/1=(z-4)/(-k and (x-10/k=(y-4)/2=(z-5)/1 are co...

    Text Solution

    |

  9. A unit vector parallel to the straight line (x-2)/3 =(3+y)/(-1)=(z-2)/...

    Text Solution

    |

  10. Find the equation of the two lines through the origin which intersects...

    Text Solution

    |

  11. If the line through the points A (k,1,-1) and B(2k,0,2) is perpendicul...

    Text Solution

    |

  12. The vector equation of the line (x-2)/(2)=(2y-5)/(-3),z=-1 is r=(2hati...

    Text Solution

    |

  13. If P(3,2,-4),Q(5,4,-6) and R(9,8,-10) are collinear, then R divides PQ...

    Text Solution

    |

  14. What is the value of n so that the angle between the lines having dire...

    Text Solution

    |

  15. The equation of motion of rockets are x=2t, y=-4t, z=4t where the time...

    Text Solution

    |

  16. The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), w...

    Text Solution

    |

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

    Text Solution

    |

  18. The length of the perpendicular drawn from the point (3,-1,11) to the...

    Text Solution

    |

  19. The point of intersection of the lines ( x + 1 )/( 3 ) = ( ...

    Text Solution

    |

  20. Find the equation of a line which passes through the point (1,1,1) ...

    Text Solution

    |