Home
Class 12
MATHS
Let veca,vecb,vecc,vecd be the position ...

Let `veca,vecb,vecc,vecd` be the position vectors of the four distinct points, P,Q,R,S respectively. If `vecb-veca=vecc=vecd`. Show that PQRS is a parallelogram.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    MODERN PUBLICATION|Exercise Exercise|500 Videos

  • UNIT TEST-4

    MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

A, B, C and D have position vectors veca, vecb, vecc and vecd , repectively, such that veca-vecb = 2(vecd-vecc) . Then

let veca , vecb and vecc be three vectors having magnitudes 1, 1 and 2, respectively, if vecaxx(vecaxxvecc)+vecb=vec0, then the acute angle between veca and vecc is _______

Let veca,vecb,vecc be the three vectors of magnitude 5, 3, I respectively. If each one is perpendicular to the sum of other two vectors, prove that |veca+vecb+vecc| = sqrt35 .

Let veca,vecb and vecc represent vectors vec(BC),vec(CA) and vec(AB) in triangleABC respectively s.t. veca+vecb+vecc=vec0 ,. Show that : vecaxxvecb=vecbxxvecc=veccxxveca .

If veca, vecb and vecc are position vectors of A,B, and C respectively of DeltaABC and if|veca-vecb|,|vecb-vec(c)|=2, |vecc-veca|=3 , then the distance between the centroid and incenter of triangleABC is

Let veca,vecb and vecc be three non-zero vectors such that no two of them are collinear and (vecaxxvecb)xxvecc=1/3|vecb||vecc|veca . If 'theta' is the angle between the vectors vecb and vecc , then a value of sin theta is :

If veca,vecb,vecc,vecd respectively, are position vectors representing the vertices A,B,C,D of a parallelogram, then write vecd in terms of veca,vecb and vecc .

Simplify : [veca-vecb,vecb-vecc,vecc-veca] .

Let veca, vecb and vecc be the three vectors having magnitudes, 1,5 and 3, respectively, such that the angle between veca and vecb "is" theta and veca xx (veca xxvecb)=vecc . Then tan theta is equal to

MODERN PUBLICATION-VECTORS-Exercise
  1. If Q is the point of intersection of the medians of a triangle ABC, pr...

    Text Solution

    |

  2. G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(G...

    Text Solution

    |

  3. Let veca,vecb,vecc,vecd be the position vectors of the four distinct p...

    Text Solution

    |

  4. Show that the line joining any vertex of a parallelogram to the mid-po...

    Text Solution

    |

  5. Prove that the figure formed by joining the mid-points of the pairs of...

    Text Solution

    |

  6. Show that if P,A,B are any three points, then lambda vec(PA)+mu vec(PB...

    Text Solution

    |

  7. Obtain the dot product of the vectors : veca=veci-hatj+hatk and vecb=v...

    Text Solution

    |

  8. Write the magnitude of a vector veca in terms of dot product.

    Text Solution

    |

  9. If veca=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk find the projectio...

    Text Solution

    |

  10. Let veca=2hati+3hatj+2hatk and vceb=hati+2hatj+hatk. Find the projecti...

    Text Solution

    |

  11. Find the projection of the vector hati-hatj on the vector hati+hatj.

    Text Solution

    |

  12. Find veca.vecb If veca=3hati-hatj+2hatk and vecb=2hati+3hatj+3hatk

    Text Solution

    |

  13. Find veca.vecb If veca=2hati-hatj+hatk and vecb=2hatj-hatk.

    Text Solution

    |

  14. Evaluate the product (3 hata-5hatb) cdot(2hata+7hatb)

    Text Solution

    |

  15. If veca is a unit vector and (vecx - veca) cdot (vecx + veca) = 8, th...

    Text Solution

    |

  16. If veca is a unit vcetor and (vecx-veca)*(vecx+veca)=80, then find |ve...

    Text Solution

    |

  17. If vecp is a unit vcetor and (vecx-vecp)*(vecx+vecp)=80, then find |ve...

    Text Solution

    |

  18. Find |vecx|, if for a unit vector veca, (vecx - veca)cdot(vecx+veca)...

    Text Solution

    |

  19. Find the angle between the vectors : hati-hatj and hatj-hatk.

    Text Solution

    |

  20. Find the angle between the vectors : hati+hatj+hatk and hati+hatj-hatk...

    Text Solution

    |