Home
Class 12
MATHS
Find the value of lamda such that the li...

Find the value of `lamda` such that the line `(x-1)/(2)=(y-1)/(3)=(z-1)/(lamda)` is `bot` to normal to the plane `vecr.(2veci+3vecj+4veck)=0`.

A

`-(13)/(4)`

B

`-(17)/(4)`

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Since line is parallel to the plane, vector `2hati+3hatj+lamdahatk` is perpendicular to the normal to the plane
`2hati + 3hatj+ 4hatk`
`rArr" "2xx2+ 3xx3 + 4lamda =0`
or `" "lamda = - (13)/(4)`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise REASONING TYPE|10 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise SUBJECTIVE TYPE|17 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the line (x-1)/3=(y-1)/2=(z-1)/4 and the plane 2x+y-3z+4=0.

Find the image of the line (x-1)/3=(y-2)/4=(z-3)/5 on the plane x-2y+z+2=0 .

Find the value of lamda so that the lines (1-x)/(3)=(7y-14)/(2lamda)=(z-3)/(2) and (7-7x)/(3lamda)=(y-5)/(1)=(6-z)/(5) are at right angles.

Find the equation of the projection of the line (x-1)/2=(y+1)/(-1)=(z-3)/4 on the plane x+2y+z=9.

Find the angle between the line (x-1)/3=(y+1)/2=(z-1)/4 and plane 2x + y - 3z + 4 = 0.

Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and the plane x+y+z+3=0.

Find the distance between the line (x+1)/(-3)=(y-3)/2=(z-2)/1 and the plane x+y+z+3=0.

The value of lamda or which the straighat line (x-lamda)/3=(y-1)/(2+lamda)=(z-3)/(-1) may lie on the plane x-2y=0 (A) 2 (B) 0 (C) -1/2 (D) there is no such lamda

Find the equations of the projection of the line (x+1)/- 2=(y-1)/3=(z+2)/4 on the plane 2x+y+4z=1

Find the value of lamda so that the straight lines: (1-x)/(3)= (7y -14)/(2 lamda)= (z-3)/(2) and (7-7x)/(3 lamda)= (y-5)/(1)= (6-z)/(5) are at right angles.

CENGAGE ENGLISH-THREE-DIMENSIONAL GEOMETRY -SINGLE CORRECT ANSWER TYPE
  1. The three planes 4y+6z=5,2x+3y+5z=5a n d6x+5y+9z=10 a. meet in a poi...

    Text Solution

    |

  2. The equation of the plane through the line of intersection of the plan...

    Text Solution

    |

  3. Equation of the plane passing through the points (2,2,1)a n d(9,3,6)...

    Text Solution

    |

  4. Find the value of lamda such that the line (x-1)/(2)=(y-1)/(3)=(z-1)/(...

    Text Solution

    |

  5. The equation of the plane passing through the intersection of x + 2y +...

    Text Solution

    |

  6. The plane 4x+7y+4z+81=0 is rotated through a right angle about its l...

    Text Solution

    |

  7. The vector equation of the plane passing through the origin and the li...

    Text Solution

    |

  8. The two lines vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxve...

    Text Solution

    |

  9. The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=...

    Text Solution

    |

  10. The direction cosines of a line satisfy the relations lambda(l+m)=n...

    Text Solution

    |

  11. The intercepts made on the axes by the plane the which bisects the ...

    Text Solution

    |

  12. Find the angle between the lines whose direction cosines are given by ...

    Text Solution

    |

  13. A sphere of constant radius 2k passes through the origin and meets t...

    Text Solution

    |

  14. A plane passes through a fixed point (a ,b ,c)dot The locus of the ...

    Text Solution

    |

  15. What is the nature of the intersection of the set of planes x+a y+(b...

    Text Solution

    |

  16. Find the equation of a straight line in the plane vecr.vecn=d which is...

    Text Solution

    |

  17. What is the equation of the plane which passes through the z-axis and ...

    Text Solution

    |

  18. A straight line L on the xy-plane bisects the angle between O Xa n dO ...

    Text Solution

    |

  19. For what value (s) of a will the two points (1,a ,1)a n d(-3,0,a) l...

    Text Solution

    |

  20. If the plane x/2+y/3+z/6=1 cuts the axes of coordinates at points, A ,...

    Text Solution

    |