IIT JEE , AIEEE Forum - Mathematics , Vectors

magiclko

m putting this question on behalf of "Karthik-abhiram"... pls solve this for him

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The position vectors a,b,c and d {all in vectors} of four points A,B,C and D

on a plane are such that

(a-d).(b-c)=(b-d).(c-a)=0, {all in vectors}

then the pont D is

1]centroid of

ABC

2] ortho centre of

ABC

3]circumcentre of

ABC

4]None of these.

plzz help ,and post a detailed solution plz and i want theoritical proof plzz as it would increase our mind to think better for other problems like these

aysh

THe answer seems 2 b
3]circumcentre of ABC.

Is it right?
If yes, I'll give the detailed solution.

DO RATE & REPLY....

karthik_abiram

i m sorry its not that.........thanx for trying........

kghedriu

Hey the answer is orthocentre option (2)

check that first of all, in all options u hav triangle ABC.....

so, keep it as fixed....

now, try for the positions of D...

the given equations imply that AD.BC=0 and BD.AC=0 (. means doy product)

so, AD and BC are perpendicular and so are BD and AC.....

for a given triangle ABC, this is possible only with the orthocentre.....

hope m clear...

thank u...

Goutham Harsha

rajat

hey kartik i already told u its : b

karthik_abiram

yea yea i just want the idea to solve these type of problems...........

avinash.sharma

Hello karthik_abiram

Most of the problems in the vector algebra are ended with only three major things

1. A line vector A (a) and B (b) are two vectors then their line vector AB is b-a

2. Dot product of two vectors a.b = |a||b| cos t

Special cases of the dot product

Since i and j and k are all one unit in length and they are all mutually perpendicular, we have

i.i = j.j = k.k = 1
and i.j = j.i = i.k = k.i = j.k = k.j = 0. As cos 0 =1

3. Cross Product

If we let the angle between A and B be

, then the cross product of A and B can be expressed as

A

B

Same way sin90=1 so you can calculate the different unit vaectors.

karthik_abiram

Thank you sir and special thanks to my didi

, for this and also for answering all the vectors.....

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