Home
Class 12
MATHS
In a triangle P Q R ,Sa n dT are points ...

In a triangle `P Q R ,Sa n dT` are points on `Q Ra n dP R ,` respectively, such that `Q S=3S Ra n dP T=4T Rdot` Let `M` be the point of intersection of `P Sa n dQ Tdot` Determine the ratio `Q M : M T` using the vector method .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos
  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of /_ Q and /_R respectively. Prove that S Q > S R .

In Figure, /_Q P R=/_P Q R and M and N are respectively on sides Q R and P R of P Q R such that Q M=P N . Prove that O P=O Q , where O is the point of intersection of P M and Q Ndot

In /_\ P Q R , M and N are points on sides P Q and P R respectively such that P M=15 c m and N R=8c m . If P Q=25 c m and P R=20 c m state whether M N || Q R .

In Figure, S and T are points on the sides P Q and P R respectively of /_\ P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of /_\P S T and /_\P Q R .

In Figure, /_Q P R=\ /_P Q R\ a n d\ M\ a n d\ N are respectively on sides Q R\ a n d\ P R of P Q R\ such that Q M=P Ndot Prove that O P=O Q , where O is the point of intersection of P M\ a n d\ Q N

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

In Figure, T is a point on side Q R of P Q R and S is a point such that R T=S Tdot Prove That : P Q+P R > Q S

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

In Figure, T Q\ a n d\ T R are the bisectors of /_Q\ a n d\ /_R respectively. If /_Q P R=80^0a n d\ /_P R T=30^0, determine /_T Q R\ a n d\ /_Q T R

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Four non –zero vectors will always be a.  linearly dependent       ...

    Text Solution

    |

  2. A boat moves in still water with a velocity which is k times less t...

    Text Solution

    |

  3. In a triangle P Q R ,Sa n dT are points on Q Ra n dP R , respectively,...

    Text Solution

    |

  4. In a quadrilateral P Q R S , vec P Q= vec a , vec Q R = vec b , vec S ...

    Text Solution

    |

  5. solve the differential equation (1+x^2)dy/dx=x

    Text Solution

    |

  6. Sow that x1 hat i+y1 hat j+z1 hat k ,x2 hat i+y2 hat j+z2 hat k ,a n d...

    Text Solution

    |

  7. The position vector of the points P and Q are 5 hat i+7 hat j-2 hat ...

    Text Solution

    |

  8. Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat...

    Text Solution

    |

  9. If vec a and vec b are two unit vectors and theta is the angle between...

    Text Solution

    |

  10. The vectors x hat i+(x+1) hat j+(x+2) hat k ,(x+3) hat i+(x+4) hat j+(...

    Text Solution

    |

  11. vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammad...

    Text Solution

    |

  12. The vector vec a has the components 2p and 1 w.r.t. a rectangular C...

    Text Solution

    |

  13. The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 ...

    Text Solution

    |

  14. If vec a , vec b , vec c are non-coplanar vector and lambda is a re...

    Text Solution

    |

  15. If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are...

    Text Solution

    |

  16. If the vectors hat i- hat j , hat j+ hat k and vec a form a triangl...

    Text Solution

    |

  17. If the resultant of three forces vec F1=p hat i+3 hat j- hat k , v...

    Text Solution

    |

  18. vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c...

    Text Solution

    |

  19. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

    Text Solution

    |

  20. Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k ...

    Text Solution

    |