Home
Class 12
MATHS
Let P(3,2,6) be a point in space and Q b...

Let `P(3,2,6)` be a point in space and `Q` be a point on line ` vec r=( hat i- hat j+2 hat k)+mu(-3 hat i+ hat j+5 hat k)dot` Then the value of `mu` for which the vector ` vec P Q` is parallel to the plane `x-4y+3z=1` is a. 1/4 b. -1/4 c. 1/8 d. -1/8

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 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

If vec (a)= 2 hat (i) - hat (j) + hat (k) and vec(b) = - hat (i) + 3 hat (j) + 4 hat (k) , then value of vec (a). vec(b) is -

Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+lambda( hat i- hat j+ hat k) and the plane vec r . dot(3 hat i- hat j+ hat k)=4.

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot(( hat i+5 hat j+ hat k))=5.

If the planes vec r ( hat i+ hat j+ hat k)=q_1, vec r ( hat i+2a hat j+ hat k)=q_2a n d vec r (a hat i+a^2 hat j+ hat k)=q_3 intersect in a line, then the value of a is a. 1 b. 1//2 c. 2 d. 0

For what values of p and q the vectors 2 hat (i) + p hat (j) - 3 hat (k) and q hat (i) - 4 hat (j) + 2 hat (k) are parallel ?

If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and vec c=z hat i+x hat j+y hat k , then vec axx( vec bxx vec c) is

find the value of x,y and z so that the vectors vec a= x hat i+ 2 hat j+z hat k and vec b = 2 hat i +y hat j +hat k are equal

Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k) a n d vec r=(5 hat j-2 hat k)+mu(3 hat i+2 hat j+6 hat k)dot

Find the point where line which passes through point (1,2,3) and is parallel to line vec r= hat i+ hat j+2 hat k+lambda( hat i-2 hat j+3 hat k) meets the xy-plane.

CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=...

    Text Solution

    |

  2. A plane which prependicular totwo planes 2x-2y+z=0and x-y+2z=4 passes ...

    Text Solution

    |

  3. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

    Text Solution

    |

  4. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersec...

    Text Solution

    |

  5. Consider a set of point R in which is at a distance of 2 units from t...

    Text Solution

    |

  6. Consider the lines L1:(x-1)/2=y/(-1)=(z+3)/1,L2:(x-4)/1=(y+3)/1=(z+3)/...

    Text Solution

    |

  7. Statement 1: A plane passes through the point A(2,1,-3)dot If distan...

    Text Solution

    |

  8. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

    Text Solution

    |

  9. If the distance between the plane Ax-2y+z=d. and the plane containing ...

    Text Solution

    |

  10. Prove that the volume of tetrahedron bounded by the planes vec rdo...

    Text Solution

    |

  11. If a variable plane forms a tetrahedron of constant volume 64k^3 with ...

    Text Solution

    |

  12. O A ,O Ba n dO C ,w i t hO as the origin, are three mutually perpen...

    Text Solution

    |

  13. Prove that for all values of lambda and mu , the planes (2x)/a+y/b+(...

    Text Solution

    |

  14. If P is any point on the plane l x+m y+n z=pa n dQ is a point on the l...

    Text Solution

    |

  15. find the equation of the plane with intercepts 2,3 and 4 on the x, y a...

    Text Solution

    |

  16. A variable plane l x+m y+n z=p(w h e r el ,m ,n are direction cosines ...

    Text Solution

    |

  17. If a line makes angles alpha,betaa n dgamma with three-dimensional c...

    Text Solution

    |

  18. A plane which is perpendicular to two planes 2x-2y+z=0 and x-y+2z = 4 ...

    Text Solution

    |

  19. Let x-ysin alpha-zsin beta=0,xsin alpha+zsin gamma-y=0 and xsin beta+y...

    Text Solution

    |

  20. The position vectors of the four angular points of a tetrahedron OABC ...

    Text Solution

    |