Vector Difference: Explained Through Parallelograms

In summary, the conversation discusses the identification of the correct diagonal in a vector diagram and how it relates to the answer choices. The initial answer was (c) none, but upon further observation and drawing of the diagonals, it was determined that the correct answer is (b). The book's answer being (a) is deemed incorrect and (b) is confirmed as the correct answer.
  • #1
subhradeep mahata
120
13
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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  • #2
Have you drawn a diagram? Identify vectors a and b and then -b.
 
  • #3
242827

It should look something like this. How should I proceed now?
 
  • #4
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.
 
  • #5
242829

I still see it as the minor diagonal of ABEF. Please help me.
 
  • #6
The answer in your book is wrong. That's why you are so confused.
 
  • #7
Oh, I see.
So what's it going to be?
I am still on (b).
 
  • #8
subhradeep mahata said:
Oh, I see.
So what's it going to be?
I am still on (b).
(b) is correct.
 
  • #9
Oh, so that's it.
I guess I have to double check every answer key now.
Thanks.
 

1. What is a vector difference?

A vector difference is the result of subtracting one vector from another. It represents the change in position or direction between the two vectors.

2. How is vector difference calculated?

Vector difference is calculated by subtracting the x, y, and z components of one vector from the corresponding components of another vector. This can be done using the head-to-tail method or by using the Pythagorean theorem.

3. What is the significance of using parallelograms to explain vector difference?

Parallelograms are used to visually represent vector difference because they illustrate the magnitude and direction of the resulting vector. This method is helpful in understanding the concept of vector difference and can be applied to real-life situations.

4. Can vector difference be negative?

Yes, vector difference can be negative. This occurs when the resulting vector points in the opposite direction of the original vectors. This can happen when subtracting a larger vector from a smaller one or when the two vectors are in opposite directions.

5. How is vector difference different from vector addition?

Vector difference and vector addition are two different operations that involve combining two vectors. Vector difference results in a new vector representing the change between the original vectors, while vector addition results in a new vector representing the combined magnitude and direction of the original vectors.

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