Home
Class 12
MATHS
If the position vectors of the points A,...

If the position vectors of the points A, B, C are `2hat(i) + hat(j) - hat(k), 3hat(i) - 2hat(j) + hat(k)` and `hat(i) + 4hat(j) - 3hat(k)` respectively, then prove that A, B, C are collinear.

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPER-5

    SHARAM PUBLICATION|Exercise EXERCISE|39 Videos

  • QUESTION PAPER 2011

    SHARAM PUBLICATION|Exercise EXERCISE|55 Videos

Similar Questions

Explore conceptually related problems

The position vectors of the point A,B,C and D are 4hat(i)+3hat(j)-hat(k),5hat(i)+2hat(j)+2hat(k),2hat(i)-2hat(j)-3hat(k) and 4hat(i)-4hat(j)+3hat(k) , respectively. Show that vec(AB) and vec(CD) are parallel.

Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

Show that the following vectors are coplanar. hat(i) - 2hat(j) + 2hat(k), 3hat(i) + 4hat(j) + 5hat(k), -2hat(i) + 4hat(j) - 4hat(k)

Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and -4 hat(i) + 3 hat(j) - hat(k) are collinear.

Show that the following vectors are coplanar. hat(i) + 2hat(j) + 3hat(k), -2hat(i) - 4hat(j) + 5hat(k), 3hat(i) + 6hat(j) + hat(k)

SHARAM PUBLICATION-QUESTION PAPER 2010-EXERCISE
  1. Find the particular solution of the following differential equation : ...

    Text Solution

    |

  2. Find an integrating factor of the differential equation (x + tan y ) d...

    Text Solution

    |

  3. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

    Text Solution

    |

  4. Find the scalar projection of the vector vec a= 3 hat i+6 hat j+9 hat ...

    Text Solution

    |

  5. Find the value of lambda such that the following vectors are coplanar...

    Text Solution

    |

  6. Bisecting the line segment joining (-1,4,3) and (5,-2,-1) at right ang...

    Text Solution

    |

  7. Proved that the line (x-1)/2=(y+2)/(-3)=(z-3)/1 lies on the plane 7x+5...

    Text Solution

    |

  8. If one end of a diameter of the sphere x^2+y^2+z^2-2x+4y-6z-11=0 is (-...

    Text Solution

    |

  9. Show that feasible region for the following constarints in a graph 2x+...

    Text Solution

    |

  10. If a system of equations lamda x +3y=0 x+(lamda-2)y=0 has infinitely...

    Text Solution

    |

  11. Find the inverse of the following : [[2,5],[1,3]]

    Text Solution

    |

  12. If the sets A and B have m and n elements respectively, then how many ...

    Text Solution

    |

  13. If A and B are any two events and AsubB, then prove that P(A)leP(B)

    Text Solution

    |

  14. If a die is thrown twice in succession, then find the probability that...

    Text Solution

    |

  15. Find (dy)/(dx) if x=y^x+tan^(-1)x.

    Text Solution

    |

  16. if y=e^(cos^(-1)x) then find dy/dx.

    Text Solution

    |

  17. Show that the rectangle of maximum area that can be inscribed in a giv...

    Text Solution

    |

  18. Determine: underset (x rarr0)lim(x cos x)/( sin x).

    Text Solution

    |

  19. Integrate: int sin 4xdx

    Text Solution

    |

  20. Evaluate int (dx)/((x+1)sqrt(1-x^2))

    Text Solution

    |