Home
Class 12
MATHS
Let ABCD be a parallelogram such that AB...

Let ABCD be a parallelogram such that AB=q, AD=p and `angleBAD` be an acute angle. If r the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by

A

`vecr=3vecq-(3(vecp*vecq))/(vecp*vecp) vecp`

B

`vecr=-vecq+((vecp*vecq))/(vecp*vecp) vecp`

C

`vecr=vecq-(((vecp*vecq))/(vecp*vecp) )vecp`

D

`vecr=-3vecq+(3(vecp*vecq))/(vecp*vecp) vecp`

Text Solution

Verified by Experts

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

Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p""a n d""/_B A D be an acute angle. If vec r is the vector that coincides with the altitude directed from the vertex B to the side AD, then vec r is given by (1) vec r=3 vec q-(3( vec pdot vec q))/(( vec pdot vec p)) vec p (2) vec r=- vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p (3) vec r= vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p (4) vec r=-3 vec q+(3( vec pdot vec q))/(( vec pdot vec p)) vec p

In fig. P is the mid point of side BC of a parallelogram ABCD such that angleBAP=angleDAP prove that AD=2CD

ABCD is a parallelogram. The circle through A,B is so drawn that it intersects AD at P and CB at Q. Prove that P,Q,C and D are concyclic.

Let vertex of an angle ABC be located outside a circle and let the sides of the angle intersect chords AD and CE with the circle. Prove that /_ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

let ABC be a right angled triangle at C. If the inscribed circle touches the side AB at D and (AD) (BD)=11, then find the area of triangle ABC. .

Let PQR be a triangle of area Delta with a = 2, b = 7//2 , and c = 5//2 , where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R, respectively. Then (2 sin P - sin 2P)/(2 sin P + sin 2P) equals

ABCD is a parallelogram. P is any point on AD, such that AP = 1/3AD and Q is a point on BC such that CQ = 1/3BC . Prove that AQCP is a parallelogram.

Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :

ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, show that: ar(BPC) = ar(DPQ)

A pyramid with vertex at point P has a regular hexagonal base ABCDEF. Position vectors of points A and B are hati and hati+ 2hatj , respectively. The centre of the base has the position vector hati+hatj+sqrt3hatk . Altitude drawn from P on the base meets the diagonal AD at point G. Find all possible vectors of G. It is given that the volume of the pyramid is 6sqrt3 cubic units and AP is 5 units.

MODERN PUBLICATION-VECTORS-Exercise
  1. If the vectors phati+hatj+hatk,hati+qhatj+hatk and hati+hatj+rhatk(p n...

    Text Solution

    |

  2. Let a,b and c be three non-zero vectors which are pairwise non-colline...

    Text Solution

    |

  3. Let veca and vecb be two unit vectors. If the vectors : vecc=veca+2vec...

    Text Solution

    |

  4. Let ABCD be a parallelogram such that AB=q, AD=p and angleBAD be an ac...

    Text Solution

    |

  5. If veca and vecb are vectors such that |veca+vecb|=sqrt(29) and vecaxx...

    Text Solution

    |

  6. If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj-4hatk are t...

    Text Solution

    |

  7. Let vec(PR)=3hati+hatj-2hatk and vec(SQ)=hati-3hatj-4hatk determine di...

    Text Solution

    |

  8. If [vecaxxvecb vecbxxvecc veccxxveca]=lambda[veca vecb vecc]^2, ...

    Text Solution

    |

  9. Let veca,vecb and vecc be three non-zero vectors such that no two of t...

    Text Solution

    |

  10. Let veca,vecb and vecc be three unit vectors such that : vecaxx(vecbxx...

    Text Solution

    |

  11. Find the values of 'x' for which x(hati+hatj+hatk) is a unit vector.

    Text Solution

    |

  12. Find the angle between the vectors hati-hatj and hatj-hatk.

    Text Solution

    |

  13. Find |vecaxxvecb| if veca=2hati+hatj+3hatk and vceb=3hati+5hatj-2hatk.

    Text Solution

    |

  14. Show that the following vectors are collinear : 2hati-3hatj+4hatk and ...

    Text Solution

    |

  15. Show that the vectors : 2hati-hatj+hatk,hati-3hatj-5hatk and 3hati-4ha...

    Text Solution

    |

  16. If |veca|=a and |vecb|=b, prove that ((veca)/(a^2)-(vecb)/(b^2))^2=((v...

    Text Solution

    |

  17. If vecr=xhati+yhatj+zhatk, find : (hatrxxhati)*(hatrxxhatj)+xy.

    Text Solution

    |

  18. Find the value of 'lambda' such that the vectors : 3hati+lambda hatj+5...

    Text Solution

    |

  19. If |veca|=3, |vecb|=4 and |vecc|=5 and each of them is perpendicular ...

    Text Solution

    |

  20. Prove that : sin(A- B) = sin A cos B -cos A sin B.

    Text Solution

    |