Home
Class 12
MATHS
Show that the lines (x-a+d)/(alpha-delt...

Show that the lines `(x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alpha+delta)`and `(x-b+c)/(beta-gamma)=(y-b)/beta=(z-b-c)/(beta+gamma)`are coplanar.

A

0

B

1

C

`sqrt(a^(2)+c^(2))`

D

`sqrt(d^(2)+f^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS|105 Videos

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|25 Videos

  • THE DIMENSIONAL GEOMETRY

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2 (SINGLE CORRECT ANSWER TYPE QUESTIONS))|16 Videos

  • STATISTICS

    MCGROW HILL PUBLICATION|Exercise QUESTION FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|13 Videos

  • TRIGONOMETRICAL IDENTITIES AND EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

Show that the lines (x-a+d)/(alpha-delta)=(y-a)/(alpha)=(z-a-d)/(alpha+delta)(x-b+c)/(beta-gamma)=(y-b)/(beta)=(z-b-c)/(beta+gamma) are coplanar.

Prove that the straight lines x/alpha=y/beta=z/gamma,x/l=y/m=z/n and x/(a alpha)=y/(b beta)=z/(c gamma) will be co planar if l/alpha(b-c)+m/beta(c-a)+n/gamma(a-b)=0

If |((beta+gamma-alpha -delta)^4 , (beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4, (gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4, (alpha + beta-gamma-delta)^2,1)|=-k(alpha -beta)(alpha -gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta) , then the value of (k)^(1//2) is ____

If alpha,beta,gamma are different from 1 and are the roots of ax^(3)+bx^(2)+cx+d=0 and (beta-gamma)(gamma-alpha)(alpha-beta)=(25)/(2) ,then prove that det[[(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)alpha,beta,gammaalpha^(2),beta^(2),gamma^(2)]]=(25d)/(2(a+b+c+d))

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

MCGROW HILL PUBLICATION-THE DIMENSIONAL GEOMETRY -EXERCISE (NUMERICAL ANSWER TYPE QUESTIONS)
  1. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alpha+...

    Text Solution

    |

  2. For a non-zero real number x, u, v, w if the points with position vect...

    Text Solution

    |

  3. If four points with position vectors A(-i+2j+3k),B(-i-12j-3k),C(2i-j-4...

    Text Solution

    |

  4. A non zero vector veca is parallel to the line of intersection of the ...

    Text Solution

    |

  5. Suppose direction cosines of two lines L(1)andL(2) are related by l+m+...

    Text Solution

    |

  6. If Q(5/3,7/3,17,3) is foot of perpendicular drawn from P(1, 0, 3) on a...

    Text Solution

    |

  7. A line passing through A(2,-1,5)andB(4,3,-10) meets the xy-plane at (x...

    Text Solution

    |

  8. A variable plane in space moves in such a way that the sum of its reci...

    Text Solution

    |

  9. If plane x + 4y - 2z = 1, x + 7y – 5z = beta, x + 5y + alphaz = 5 in...

    Text Solution

    |

  10. Suppose a and b lie on a plane normal to the plane containing c and d....

    Text Solution

    |

  11. A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(-1,1,2) and O(0,0,0). T...

    Text Solution

    |

  12. The length of the perpendicular from the point (2, -1, 4) on the strai...

    Text Solution

    |

  13. If a point R(4,y,z) lies on the line segment joining the points P(2,-3...

    Text Solution

    |

  14. The vertices B and C of a DeltaABC lie on the line, (x+2)/(3)=(y-1)/(0...

    Text Solution

    |

  15. If the plane 2x-y+2x+3=0 has the distances (1)/(3) and (2)/(3) units f...

    Text Solution

    |

  16. The distance of the point having position vector -hati+ 2 hatj + 6 hat...

    Text Solution

    |

  17. Let V = Volume of the tetrahedron whose vertices are A(1,0,0),B(0,0,1)...

    Text Solution

    |

  18. If the symmetrical form of line of intersection of planes 4x-3y=1,2y-4...

    Text Solution

    |

  19. Let d = the distance of point A(4,1,1) from the line of intersection o...

    Text Solution

    |

  20. If equation of the plane through the parallel lines (x+1)/(3)=(y-2)/...

    Text Solution

    |