Home
Class 12
MATHS
Show that the four points A, B, C and D...

Show that the four points A, B, C and D with position vectors`4 hat i+5\ hat j+ hat k ,-(\ hat j+ hat k),3 hat j+9\ hat j+4 hat k\ a n d\ 4( hat i+ hat j+ hat k)`, respectively are coplanar.

Promotional Banner

Topper's Solved these Questions

  • EXAM REVISION SERIES

    XII BOARD PREVIOUS YEAR PAPER ENGLISH|Exercise All Questions|19 Videos

Similar Questions

Explore conceptually related problems

Find the value of lambda so that the four points, A, B, C and D with position vectors 4 hat i+5 hat j+ hat k ,- hat j- hat k ,3 hat i+lambda hat j+4 hat k and -4 hat i+4 hat j+4 hat k respectively are coplanar.

Show that the four points with position vectors 4 hat i+8 hat j+12 hat k ,\ 2 hat i+4\ hat j+6 hat k ,3 hat i+5\ hat j+4 hat k\ a n d\ 5 hat i+8\ hat j+5 hat k are coplanar.

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k vec b = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively form the vertices of a right angled triangle.

Area of a rectangle having vertices A, B, C and D with position vectors - hat i+1/2 hat j+4 hat k , hat i+1/2 hat j+4 hat k , hat i-1/2 hat j+4 hat k and - hat i-1/2 hat j+4 hat k respectively is(A) 1/2 (B) 1 (C) 2 (D) 4

The four points whose position vector are 6 hat i - 7 hat j,16 hat i - 29 hat j - 4 hat k, 3 hat j - 6 hat k, 2 hat i + 5 hat j + 10 hat k are coplanar

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

If three points A, B and C with position vectors hat(i) + x hat(j) +3 hat(k) , 3 hat(i) + 4 hat(j) + 7hat( k) and y hat(i) - 2 hat(j) - 5 hat(k) respectively are collinear, then (x,y) =

Show that the four points having position vectors 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k ,2 hat i-5 hat j+10 hat k are coplanar.

Show that the points A, B and C with position vectors, veca=3 hat i-4 hat j-4 hat k , vecb=2 hat i- hat j+ hat k and vecc= hat i-3 hat j-5 hat k respectively form the vertices of a right angled triangle.

Find the value of lambda for which the four points with position vectors hat j- hat k ,\ 4 hat i+5 hat j+lambda hat k ,\ 3 hat i+9 hat j+4 hat k\ a n d-4 hat i+4 hat j+4 hat k are coplanar.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the area of the region in the first quadrant enclosed by the y-ax...

    Text Solution

    |

  2. Evaluate : int0^(pi/2)(dx)/(1+sqrt(tanx))

    Text Solution

    |

  3. Show that the four points A, B, C and D with position vectors4 hat i+...

    Text Solution

    |

  4. Find the shortest distance between the lines vec r=( hat i+2 hat j+ h...

    Text Solution

    |

  5. Find the derivative of (sinx)^x+sin^(-1)sqrt(x) w.r.t. x

    Text Solution

    |

  6. If y=(xcos^(-1)x)/(sqrt(1-x^2))-logsqrt(1-x^2), then prove that (dy)/(...

    Text Solution

    |

  7. Find int((x^2+1)e^x)/((x+1)^2)dx

    Text Solution

    |

  8. If x=asec^3theta,y=atan^3theta, find (d^2y)/(dx^2) at theta=pi/4

    Text Solution

    |

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

    Text Solution

    |

  10. Prove that : tan^(-1)(63/16)=sin^(-1)\(5/13)+cos^(-1)(3/5)

    Text Solution

    |

  11. A tank with rectangular base and rectangular sides open at the top is ...

    Text Solution

    |

  12. Let f: N -> R be a function defined as f(x)=4x^2+12 x+15. Show that f:...

    Text Solution

    |

  13. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

    Text Solution

    |

  14. Find the minimum value of (a x+b y), where x y=c^2dot

    Text Solution

    |

  15. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

    Text Solution

    |

  16. Using properties of determinants, prove the following: |[1,a,a^2],[a^2...

    Text Solution

    |

  17. Solve the following differential equation : (sqrt(1+x^2+y^2+x^2y^2))d...

    Text Solution

    |

  18. If a=[[5,6,-3],[-4,3,2],[-4,-7,3]], then write the cofactor of the e...

    Text Solution

    |

  19. Write the sum of the order and degree of the differential equation ...

    Text Solution

    |

  20. Write the solution of the differential equation (dy)/(dx)=2^(-y)

    Text Solution

    |