Home
Class 12
MATHS
Statement 1 : If three point P, Q and R ...

Statement 1 : If three point P, Q and R have position vectors `veca, vecb and vecc`, respectively, and `2 veca + 3vecb - 5vecc=0`, then the point P, Q and R must be collinear.
Statement 2 : If for three points A, B and C, `vec(AB) = lamda vec(AC)`, then points A, B and C must be collinear.

Promotional Banner

Topper's Solved these Questions

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

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

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If vec(AO)+vec(OB)=vec(BO)+vec(OC) , show that the points A, B and C are collinear.

If three unit vectors veca, vecb and vecc " satisfy" veca+vecb+vecc= vec0 . Then find the angle between veca and vecc .

If three unit vectors veca, vecb and vecc " satisfy" veca+vecb+vecc= vec0 . Then find the angle between vecb and vecc .

A, B C and D are four points in a plane with position vectors, veca, vecb, vecc and vecd respectively, such that (veca-vecd).(vecb-vecc)= (vecb-vecd).(vecc-veca)=0 then point D is the ______ of triangle ABC.

Let A(z_1),B(z_2) and C(z_3) be the three points in Argands plane The point A B and C are collinear if

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

The position vector of a point A is veca+2vecb and veca divides AB internally in the ratio 2:3 , then the position vector of the point B is -

If vec a , vec ba n d vec c are three non coplanar vectors, then ( veca + vecb + vecc )[( veca + vecb )×( veca + vecc )] is :

Define the position vector of a point with respect to an origin. If vec(a) " and " vec(b) are the position vectors of the points P and Q respectively, find the vector vec(PQ) in terms of vec(a) " and " vec(b) .

Show that the points P(-2,3,5) ,Q (1,2,3) and R (7,0,-1) are collinear

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammad...

    Text Solution

    |

  2. A vector oversetrarra has components 2p and 1 with respect to a rectan...

    Text Solution

    |

  3. Statement 1 : If three point P, Q and R have position vectors veca, ve...

    Text Solution

    |

  4. In a four-dimensional space where unit vectors along the axes are h...

    Text Solution

    |

  5. Let A B C be a triangle, the position vectors of whose vertices are -1...

    Text Solution

    |

  6. If non-zero vectors vec a and vec b are equally inclined to coplanar ...

    Text Solution

    |

  7. If A(-4,0,3) and B(14 ,2,-5), then which one of the following points l...

    Text Solution

    |

  8. Prove that the sum of three vectors determined by the medians of a ...

    Text Solution

    |

  9. Prove that the resultant of two forces acting at point O and repres...

    Text Solution

    |

  10. Two forces vec A B and vec A D are acting at vertex A of a quadrilat...

    Text Solution

    |

  11. ABC is a triangle and P any point on BC. If vec(PQ) is the sum of vec(...

    Text Solution

    |

  12. If vector vec a+ vec b bisects the angle between vec a and vec b , ...

    Text Solution

    |

  13. ABCDE is a pentagon. Prove that the resultant of force vec A B , vec...

    Text Solution

    |

  14. if vec (AO) + vec (O B) = vec (B O) + vec (O C) ,than prove that B...

    Text Solution

    |

  15. A unit vector of modulus 2 is equally inclined to x- and y-axes at an ...

    Text Solution

    |

  16. Find the equations of the normal to the curve y=x^3+2x+6 which are par...

    Text Solution

    |

  17. Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- ...

    Text Solution

    |

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

    Text Solution

    |

  19. Let vec a , vec b , vec c , vec d be the position vectors of the four...

    Text Solution

    |

  20. Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such...

    Text Solution

    |