Home
Class 12
MATHS
Find the equation of a line : passing th...

Find the equation of a line : passing through the point `vec c` , parallel to the plane `vec r *vec n = p` and intersecting the line `vec r =vec a + t vec b`.

Text Solution

Verified by Experts

The correct Answer is:
`vecr=vec c +k n xx (vecn -veca)xx vecb)]`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos
  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|87 Videos
  • THREE DIMENSIONAL GEOMETRY

    VMC MODULES ENGLISH|Exercise LEVEL-1|90 Videos
  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos
  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

The equation of a line passing through the point vec a parallel to the plane vec r. vec n=q and perpendicular to the line vec r= vec b+t vec c is a. vec r= vec a+lambda( vec nxx vec c) b. ( vec r- vec a)xx( vec nxx vec c) c. vec r= vec b+lambda( vec nxx vec c) d. none of these

The vector equation of the plane passing through the origin and the line of intersection of the planes vec rdot vec a=lambdaa n d vec rdot vec b=mu is (a) vec rdot(lambda vec a-mu vec b)=0 (b) vec rdot(lambda vec b-mu vec a)=0 (c) vec rdot(lambda vec a+mu vec b)=0 (d) vec rdot(lambda vec b+mu vec a)=0

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

Find the equation of a straight line in the plane vec r* vec n=d which is parallel to vec r= vec a+lambda vec b and passes through the foot of the perpendicular drawn from point P( vec a)to vec rdot vec n=d(w h e r e vec ndot vec b=0)dot a. vec r= vec a+((d- vec a*vec n)/(n^2))n+lambda vec b b. vec r= vec a+((d- vec a* vec n)/n)n+lambda vec b c. vec r= vec a+(( vec a* vec n-d)/(n^2))n+lambda vec b d. vec r= vec a+(( vec a* vec n-d)/n)n+lambda vec b

The expression in the vector form for the point vec r_1 of intersection of the plane vec rdot vec n=d and the perpendicular line vec r= vec r_0+t vec n where t is a parameter given by

Write the position vector of the point where the line vec r= vec a+lambda vec b meets the plane vec r dot (vec n)=0.

The equation of the plane which passes through the line of intersection of planes vec r. vec n_1=, q_1, vec r. vec n_2=q_2 and the is parallel to the line of intersection of planers vec r. vec n_3=q_3a n d vec r. vec n_4-q_4 is

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

The equation of the plane which passes through the line of intersection of planes vec rdot vec n_1=, q_1, vec rdot vec n_2=q_2 and the is parallel to the line of intersection of planers vec rdot vec n_3=q_3a n d vec rdot vec n_4-q_4 is

P is a point on the line through the point A whose position vector is vec a and the line is parallel to the vector vec b . If P A=6, the position vector of P is: (a) vec a+6 vec b (b) vec a+6/(| vec b|) vec b (c) vec a-6 vec b/(| vec b|) (d) vec b+6/(| vec a|) vec a

VMC MODULES ENGLISH-THREE DIMENSIONAL GEOMETRY -LEVEL-2
  1. A plane makes interceptsOA, OB and OC whose measurements are a, b and ...

    Text Solution

    |

  2. Let vectors veca, vecb veca and vecd be such that (veca xxvecb)xx (vec...

    Text Solution

    |

  3. The image of plane p (1) in the plane mirror p (2) is : Let two planes...

    Text Solution

    |

  4. Find the equation of a line : passing through the point vec c , paral...

    Text Solution

    |

  5. Find the equation of a line passing through the point vec c, parallel ...

    Text Solution

    |

  6. Prove that the shortest distance between the diagonals of a rectangula...

    Text Solution

    |

  7. The equation of the plane which passes through the line of intersect...

    Text Solution

    |

  8. Find the equation a plane containing the line vecr =t veca and perpend...

    Text Solution

    |

  9. Prove that the line of intersection of x + 2y + 3z=0 and 3x + zy+ z=0 ...

    Text Solution

    |

  10. Find the distance of the point (3,8,2) from the line vecr=hati + 3 hat...

    Text Solution

    |

  11. Find the vector equation of the plane vecr = 2 hati + hatj - 3 hatk + ...

    Text Solution

    |

  12. Show that the equation to the plane containing the line y/b+ z/c =1, x...

    Text Solution

    |

  13. Prove that the volume of the tetrahedron and that formed by the centro...

    Text Solution

    |

  14. In a regular tetrahedron, prove the following: The angle between any e...

    Text Solution

    |

  15. In a regular tetrahedron, prove that angle theta between any edge and ...

    Text Solution

    |

  16. A line L1 passing through a point with position vector p=i+2j+3k and ...

    Text Solution

    |

  17. A line L1 passing through a point with position vector p=i+2h+3k and ...

    Text Solution

    |

  18. For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly inter...

    Text Solution

    |

  19. Find area parallelogram lines y=mx, y=mx+1, y=nx and y=nx+1 equal to:

    Text Solution

    |

  20. For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly inter...

    Text Solution

    |