Vector Help

[Nikesh]

Somebody plz provide me some important notes on Three Dimensional Vector.........

 

[XPFMember]

Assalamoalaikum!!
Well if u have any doubts in specific let me know..i'll try to post a few revision notes soon!

 

[Nikesh]

there is no specific but post ur revision notes soon as possible ......

 

[XPFMember]

wll try...actually there's just a few points to keep in mind ...that's all...and btw i'm gonna post what i've understood ...is that ok 4 u?

 

[Nikesh]

ya its ok for me!!!!!!!!!!

 

[wahab305]

just remember on thing while drawing vectors if two vectors are clockwise then resultant anticlockwise and vice versa

 

[XPFMember]

Assalamoalaikum!!

Finally m here to post the notes


Well it is written as a column vector with 2 rows...ofcourse that u know
Eg OA =

• (3)
  (4)
  (6)

it can be written as 3i + 4j + 6k

Lets say OA is as said above and OB is 2i + 7j +3k

Now First thing is Addition

• Add the corresponding terms..i and i ..j and j ...k and k...or simple write them as column vector and follow the steps to add to vectors!
  
  Then finding AB...write an eqn...the same we do for normal vectors! so AB = AO + OB and of course not to mention...reverse the signs of OA to get AO and next how i just told to add vectors in this case
  
  Let us work out AB using the vectors given above
  
  (Remember if the question states the vector as a column vector u should also give ur answer in that form and if its i,j,k then u also use that form..unless specified)
  
  So AB = AO + OB = ( 3 + 2 ) i + ( 4 + 7 ) j + ( 6 + 3) k = 5i + 11j + 9k
  

So now let us come to multiplication

• First remember a few points
  • i.j = j.k = i.k = 0 i hope u know multiplication of these vectors are known as dot product!
    i^2 =j^2=k^2 = 1
  
  if u use the expansion method of multiplying ( a i + b j + c k ) x ( p i + q j + r k ) and then simplifu using these 2 rules i just mentioned ...u will find that for this case in short we can just multiply the corresponding coeeficients of i j and k to get the dot product of two vectors..
  
  hence in this case to find the dot product OA.OB => 3(2) + 4(7) + 6(3) = 6 + 28 +18 = 52
  
  And if the two vectors are perpendicular their dot product will be equal to zero!! => Remember this rule..it's important!

Then finding the angle between two vectors

• cos AOB = (OA.OB)/(|OA||OB|)
  
  now here dont confuse with which sides to take...refer to the angle ....see the middle letter...If it's AOB as in this case... start with the middle and then th right and left...that is OA and OB
  if it's PQR so QP and QR
  
  Now |OA| will be just squaring each term and add them together and take the square root!
  |OA| = √(x^2+y^2+ z^2 )...u can leave out the i's j's and k's for the reason that we know the square of that is 1 and multiplying a no. with makes no difference!

Then there is a rule for parallel vectors..the ratio of corresponding terms must always be same if the vectors are parallel => x1/x2 = y1/y2 = z1/z2

..and finally finding unit vector in the direction of OA ...or anything...if like it's OA it'll be OA/|OA| ...and dont forget to take any common out in OA and simpligy with |OA| if possible!!



Well I think i have not left out anything!!

Hope this helps

If u have any doubts regarding any rule or anything...feel free to ask...btw sorry 4 late reply!

 

[XPFMember]

Somebody plz provide me some important notes on Three Dimensional Vector.........

did my explanation help??

 

[Nikesh]

somehow helped and thanks for ur explanation!!!!

 

[XPFMember]

somehow helped and thanks for ur explanation!!!!

:shock: i wish it cud have helped u much!!

anyways ur doubts are most welcome...areas which confuse u or anything..dont hesitate to ask