Home
Class 12
MATHS
Find the vector equation of the plane...

Find the vector equation of the plane passing through the points `(2,\ 1,\ 1)\ a n d\ (1,\ 3,\ 4)` and perpendicular to the plane `x\ -\ 2y+4z=10` . Also show that the plane thus obtained contains the line ` vec r=- hat i+3 hat j+4 hat k+lambda\ (3 hat i-2 hat j-\ 5 hat k)dot`

Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x-2y+4z=1. Also show that the plain thus obtained contains the line vec r=- hat i+3 hat j+4 hat k+lambda(3 hat i-2 hat j-5 hat k)dot

Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x-5y-15=0. Also, show that the plane thus obtained contains the line vec r= hat i+3 hat j-2 hat k+lambda( hat i- hat j+ hat k)dot

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

Find the vector equation of plane passing through the points 2hat i+hat j-hat k and -hat i+3hat j+4hat k and perpendicular to the plane vec r*(hat i-2hat j+4hat k)=10

Write the vector equation of the plane passing through the point (a,b,c) and parallel to the plane vec r.(hat i+hat j+hat k)=2

Prove that the plane vec r=(hat i+2hat j-hat k)=3 contains the line vec r=hat i+hat j+lambda(2hat i+hat j+4hat k)

Write the vector equation of the plane,passing through the point (a,b,c) and parallel to the plane vec r*(hat i+hat j+hat k)=2

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k+)lambda(3hat i-hat j-5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i-2hat j-5hat k)

Find the equation of the plane passing through the point (1,1,1) and containing the line vec r=(-3hat i+hat j+5hat k)+lambda(3hat i-hat j5hat k) Also,show that the plane contains the lines vec r=(-hat i+2hat j+5hat k)+lambda(hat i2hat j5hat k)

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. In a certain college, 4% of boys and 1% of girls are taller than 1....

    Text Solution

    |

  2. A company produces soft drinks that has a contract which requires t...

    Text Solution

    |

  3. Find the vector equation of the plane passing through the points (2...

    Text Solution

    |

  4. Evaluate the following int0^(3/2)|xcospix\ |\ dxdot

    Text Solution

    |

  5. Find the area of the region in the first quadrant enclosed by x-a xi s...

    Text Solution

    |

  6. Show that the altitude of the right circular cone of maximum volume ...

    Text Solution

    |

  7. Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4

    Text Solution

    |

  8. Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2

    Text Solution

    |

  9. If vecalpha=3 hat i+4 hat j+5 hat k and vecbeta=2 hat i+ hat j-\ 4 h...

    Text Solution

    |

  10. Evaluate : int(cosx)/((2+sinx)dx\ (3+4sinx)

    Text Solution

    |

  11. If [[1,2],[3,4]] [[3,1],[2,5]]=[[7,11],[k,23]], then write the value o...

    Text Solution

    |

  12. Find the particular solution of the differential equation. (dy)/(dx...

    Text Solution

    |

  13. Show that f\ : NvecN ,\ given by f(x)={x+1, if\ x\ i s\ od dx-1,\ \ ...

    Text Solution

    |

  14. Evaluate : int(logx)/x\ dxdot

    Text Solution

    |

  15. What is the value of the determinant |(0,2,0),(2,3,4),(4,5,6)|?

    Text Solution

    |

  16. What is the degree of the following differential equation? 5x\ ((d...

    Text Solution

    |

  17. What is the range of the function f(x)=(|x-1|)/((x-1))?

    Text Solution

    |

  18. If A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]], then for what val...

    Text Solution

    |

  19. What is the principal value of sin^(-1)(-(sqrt(3))/2)\ ?

    Text Solution

    |

  20. Find the equation of the plane through the points (2, 1, 1) and (1,...

    Text Solution

    |