Home
Class 12
MATHS
Find the vector equation of a line pas...

Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to the plane `3x-4y+5z=8.`

Text Solution

Verified by Experts

The given plane `3x-4y+5z=8 or (3hati-4hatj+5hatk)*(xhati+yhatj+7hatk)=8.`
This shows that `vecd=3hati-4hatj+5hatk` is normal to the given plane.
Therefore, the required line is parallel to `3hati-4hatj+5hatk`.
Since the required line passes through `3hati-5hatj+7hatk`, its equation is given by
`" "vecr=3hati-5hatj+7hatk+lamda(3hati-4hatj+5hatk),` where `lamda` is a parameter.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

Find the vector equation of a plane through the point hati+ hat j+hat k and parallel to the plane vecr.(2 hat i-hatj +2 hatk)=5 .

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r.( hat i- hat j+2 hat k)=5a n d vec r.(3 hat i+ hat j+ hat k)=6.

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

Find the unit vector perpendicular to the plane vec r.(2 hat i+ hat j+2 hat k)=5.

Find the vector equation of a line which passes through the point with position vector hat(i)-2hat(j)+4hat(k) and is in the direction of hat(i)+2hat(j)-hat(k) . Also, reduce it to cartesian from.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If the straight lines x=1+s ,y=-3-lambdas ,z=1+lambdasa n dx=t/2,y=1+t...

    Text Solution

    |

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

    Text Solution

    |

  3. Find the vector equation of a line passing through 3 hat i-5 hat j+7...

    Text Solution

    |

  4. Find the equation of the plane passing through the point (2,3,1) ha...

    Text Solution

    |

  5. Find the equation of the plane through the points (2, 3, 1) and (4, -5...

    Text Solution

    |

  6. Find the equation of the image of the plane x-2y+2z-3=0 in plane x+...

    Text Solution

    |

  7. Find the equation of a plane which passes through the point (1, 2, 3) ...

    Text Solution

    |

  8. Find the equation of a plane which is parallel to the plane x-2y+2z=5 ...

    Text Solution

    |

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

    Text Solution

    |

  10. Find the equation of the plane which passes through the point (1,2,...

    Text Solution

    |

  11. Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+la...

    Text Solution

    |

  12. Find the equation of the plane passing through the line (x-1)/(5)=(y+2...

    Text Solution

    |

  13. Find the equation of the plane perpendicular to the line (x-1)/2=(y...

    Text Solution

    |

  14. Find the equation of the plane passing through the straight line (x...

    Text Solution

    |

  15. Find the equation of the line drawn through the point (1, 0,2) to meet...

    Text Solution

    |

  16. If vecr=(hati+2hatj+3hatk)+lambda(hati-hatj+hatk) and vecr=(hati+2hatj...

    Text Solution

    |

  17. Find the coordinates of a point on the (x-1)/2=(y+1)/(-3)=z atg a d...

    Text Solution

    |

  18. Line L1 is parallel to vector vecalpha=-3 hat i+2 hat j+4 hat k and p...

    Text Solution

    |

  19. Find the values p so that line (1-x)/3=(7y-14)/(2p)=(z-3)/2a n d(7-7x)...

    Text Solution

    |

  20. Find the angel between the following pair of lines: vec r=2 hat i...

    Text Solution

    |