Home
Class 12
MATHS
The length of the perpendicular form ...

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|)`

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

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= a. 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= a. [ vec a\ vec b\ vec c] b. 0 c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

If axx(bxxc)=(axxb)xxc , then a. ( vec cxx vec a)xx vec b= vec0 b. vec cxx( vec axx vec b)= vec0 c. vec bxx( vec cxx vec a) =0 d. ( vec cxx vec a)xx vec b= vec bxx( vec cxx vec a)= vec0

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) a. [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

If vec a . vec b=beta and vec axx vec b= vec c ,then vec b is ((beta vec a- vec axx vec c))/(| vec a|^2) b. ((beta vec a+ vec axx vec c))/(| vec a|^2) c. ((beta vec c- vec axx vec c))/(| vec a|^2) d. ((beta vec a+ vec axx vec c))/(| vec a|^2)

Prove that [ vec l vec m vec n][ vec a vec b vec c]=| (vec l. vec a, vec l. vec b, vec l.vec c), (vec m. vec a, vec m. vec b, vec m.vec c),( vec n. vec a, vec n. vec b, vec n.vec c)| .

CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. The value of m for which straight lein 3x-2y+z+3=0=4 x-3y+4z+1 is pa...

    Text Solution

    |

  2. Let the equations of a line and plane be (x+3)/2=(y-4)/3=(z+5)/2a n...

    Text Solution

    |

  3. The length of the perpendicular form the origin to the plane passin...

    Text Solution

    |

  4. In a three-dimensional xyz space, the equation x^(2)-5x+6=0 represents

    Text Solution

    |

  5. The line (x-2)/3=(y+1)/2=(z-1)/-1 intersects the curve x y=c^(2),z=0 i...

    Text Solution

    |

  6. A unit vector parallel to the intersection of the planes vec r. \ (...

    Text Solution

    |

  7. Let L1 be the line vec r1=2 hat i+ hat j- hat k+lambda(hat i+2 hat k)...

    Text Solution

    |

  8. The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), w...

    Text Solution

    |

  9. The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-l...

    Text Solution

    |

  10. Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda...

    Text Solution

    |

  11. Column I, Column II The coordinates of a point on the line x=4y+...

    Text Solution

    |

  12. The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambd...

    Text Solution

    |

  13. Find the angle between the line (x-1)/3=(y-1)/2=(z-1)/4 and the pla...

    Text Solution

    |

  14. Find the equation of a line which passes through the point (2,3,4) ...

    Text Solution

    |

  15. Statement 1: There exist two points on the (x-1)/1=y/(-1)=(z+2)/2 w...

    Text Solution

    |

  16. Statement 1: The shortest distance between the lines x/(-3)=(y-1)/1=(z...

    Text Solution

    |

  17. Find the number of sphere of radius r touching the coordinate axes...

    Text Solution

    |

  18. Find the distance of the z-axis from the image of the point M(2-3,3...

    Text Solution

    |

  19. A line with direction cosines proportional to 1,-5, a n d-2 meets li...

    Text Solution

    |

  20. If the planes vec r ( hat i+ hat j+ hat k)=q1, vec r ( hat i+2a hat j...

    Text Solution

    |