Vector Difference: Explained Through Parallelograms

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SUMMARY

The discussion centers on the geometric representation of vector addition using parallelograms. Participants analyze the relationship between two vectors, a and b, and their resultant vector, which is depicted as the major diagonal of a parallelogram. Confusion arises regarding the identification of the diagonals, with one participant initially believing the answer to be (c) none, then switching to (b), while the correct answer is confirmed as (a) according to the textbook. Ultimately, the consensus is that the correct identification of the diagonals is crucial for understanding vector addition.

PREREQUISITES
  • Understanding of vector addition and subtraction
  • Familiarity with geometric representations of vectors
  • Knowledge of parallelogram properties
  • Ability to interpret vector diagrams
NEXT STEPS
  • Study vector addition using the parallelogram law
  • Explore vector subtraction and its geometric implications
  • Learn about the properties of diagonals in parallelograms
  • Practice drawing vector diagrams for various vector combinations
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Students of physics and mathematics, educators teaching vector concepts, and anyone seeking to deepen their understanding of vector geometry.

subhradeep mahata
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Homework Statement
The angle between two vectors a and b (along the adjacent sides of a parallelogram) is an acute angle. The vector a-b will be (a)major diagonal of parallelogram (b)minor diagonal of parallelogram (c)none
Relevant Equations
Vector diagram
We know that the sum of the two vectors is represented by the major diagonal.
Now, if I draw the vector diagram, it turns out to be a diagonal of an entirely different parallelogram. So, my first answer was (c) none.
But, I noticed that when parallelly shifted, it turns out to be the minor diagonal of the above parallelogram. So, I switched to (b).
But the correct answer according to my book is (a).
Can anyone explain this?
 
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Have you drawn a diagram? Identify vectors a and b and then -b.
 
242827

It should look something like this. How should I proceed now?
 
subhradeep mahata said:
View attachment 242827
It should look something like this. How should I proceed now?
Complete the parallelogram and draw its diagonals. Then you you will see what's going on.
 
242829

I still see it as the minor diagonal of ABEF. Please help me.
 
The answer in your book is wrong. That's why you are so confused.
 
Oh, I see.
So what's it going to be?
I am still on (b).
 
subhradeep mahata said:
Oh, I see.
So what's it going to be?
I am still on (b).
(b) is correct.
 
Oh, so that's it.
I guess I have to double check every answer key now.
Thanks.
 

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