Home
Class 12
MATHS
Find the value of lambda for which the l...

Find the value of `lambda` for which the line `(x-1)/2=(y-1)/3=(z-1)/lambda` is parallel to the plane `vecr.(2hati+3hatj+4hatk)=4`.

Text Solution

Verified by Experts

The correct Answer is:
`lambda=-13/4`
Promotional Banner

Topper's Solved these Questions

  • THE PLANE

    RS AGGARWAL|Exercise Objective Questions|35 Videos

  • THE PLANE

    RS AGGARWAL|Exercise Exercise 28I|9 Videos

  • SYSTEM OF LINEAR EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|53 Videos

  • VECTOR AND THEIR PROPERTIES

    RS AGGARWAL|Exercise Exercise 22|24 Videos

Similar Questions

Explore conceptually related problems

The value of m for which the line (x-1)/2=(y-1)/3=(z-1)/m is perpendicular to normal to the plane vecr.(2hati+3hatj+4hatk)=0 is

Find the value of m for which the line vecr.=(hati+2hatk)+lambda(2hati-mhatj-3hatk) is parallel to the plane vecr.(mhati+3hatj+hatk)=4 .

Find the value of 'm' for which the line vecr = hati+lambda(2hati-mhatj-3hatk) is parallel to the plane vecr.(mhati+3hatj+hatk) = 1 .

Find the value of m for which the line vecr.=(hati+2hatj-hatk)+lambda(2hati+hatj+2hatk) is parallel to the plane vecr.(3hati-2hatj+mhatk)=12

Find the value of 'm' for which the line vecr= (hati+2hatj-hatk)+lambda(2hati+hatj+hatk) is parallel to the plane vecr.(3hati-2hatj+mhatk) = 5 .

Find the equation of the plane through (3,4,-1) which is parallel to the plane vecr.(2hati-3hatj+5hatk)+7=0

Show that the line vecr=(4hati-7hatk)+lambda(4hati-2hatj+3hatk) is parallel to the plane vecr.(5hati+4hatj-4hatk)=7 .

Find the value of lambda for which the given planes are perpendicular to the each other: i) vecr.(2hati-hatj-lambdak)=7 and vecr.(3hati+2hatj+2hatk)=9 ii) vecr.(lambdahati+2hatj+3hatk)=5 and vecr.(hati+2hatj-7hatk)+11=0

Show that the line vecr=(2hati-2hatj+3hatk)+lambda(hati-hatj+4hatk) is parallel to the plane vecr.(hati+5hatj+hatk)=7 .

Find the value of 'm' for which the line vec(r) = ( hati + 2 hatk ) + lambda (2 hati - m hatj - 3 hatk) is parallel to the plane vec(r).(m hati + 3 hatj + hatk ) = 4.

RS AGGARWAL-THE PLANE-Exercise 28J
  1. The equation of a plane parallel to x-axis is

    Text Solution

    |

  2. Write the intercept cut off by the plane 2x+y-z=5 on x-a xi sdot

    Text Solution

    |

  3. Write the intercepts made by the plane 4x-3y+2z=12 on the coordinate a...

    Text Solution

    |

  4. Reduce the equation 2x-3y+5z+4=0 to intercept form and find the interc...

    Text Solution

    |

  5. Find the equation of a plane passing through the points A(a,0,0), B(0,...

    Text Solution

    |

  6. Write the value of k for which the planes 2x-5y+kz=4 and x+2y-z=6 are ...

    Text Solution

    |

  7. Find the angle between the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7...

    Text Solution

    |

  8. Find the angle between the planes vecr.(hati+hatj)=1 and vecr.(hati+ha...

    Text Solution

    |

  9. Find the angle between the planes vecr.(3hati-4hatj+5hatk)=0 and vecr....

    Text Solution

    |

  10. Find the angle between the line (x+1)/2=y/3=(z-3)/6and the plane 10 ...

    Text Solution

    |

  11. Find the angle between the line vecr=(hati+hatj-2hatk)+lambda(hati-hat...

    Text Solution

    |

  12. Find the value of lambda such that the line (x-2)/6=(y-1)/lambda=(z+5)...

    Text Solution

    |

  13. Find the equation of the plane passing through (a,b,c) and paralle tot...

    Text Solution

    |

  14. Find the length of the perpendicular drawn from the origin to the p...

    Text Solution

    |

  15. Find the direction cosines of the perpendicular from the origin to th...

    Text Solution

    |

  16. Show that the line vecr=(4hati-7hatk)+lambda(4hati-2hatj+3hatk) is par...

    Text Solution

    |

  17. Find the length of perpendicular from the origin to the plane vecr.(2h...

    Text Solution

    |

  18. Find the value of lambda for which the line (x-1)/2=(y-1)/3=(z-1)/lamb...

    Text Solution

    |

  19. Write the angle between the line (x-1)/2=(y-2)/1=(z+3)/-2 and the plan...

    Text Solution

    |

  20. Write the equation of a plane passing through the point (2,-1,0) and p...

    Text Solution

    |