Geometric vs Componentwise Vector Addition

In summary, the given conditions (A - F) must be true in order for expressions 1 and 2 to define the same vector C_vec as expressions 3 and 4. These conditions include: 1) giving the same length and direction for C_vec, 2) giving the same length and x component for C_vec, 3) giving the same direction and x component for C_vec, 4) giving the same length and y component for C_vec, 5) giving the same direction and y component for C_vec, and 6) giving the same x and y components for C_vec.
  • #1
linie18
2
0

Homework Statement



Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4?

1. The two pairs of expressions give the same length and direction for C_vec.
2. The two pairs of expressions give the same length and x component for C_vec.
3. The two pairs of expressions give the same direction and x component for C_vec.
4. The two pairs of expressions give the same length and y component for C_vec.
5. The two pairs of expressions give the same direction and y component for C_vec.
6. The two pairs of expressions give the same x and y components for C_vec.

Homework Equations



1. C=\sqrt{A^2 +B^2 -2 A B \cos(c)},
2. \phi = \sin^{-1}\left(\frac{B\sin(c)}{C}\right).
3. C_x = A + B\cos(\theta),
4. C_y = B\sin(\theta).

The Attempt at a Solution



I thought it would be one where you knew exactly what the vector was like AF and I don't know what I'm missing.
 
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  • #2
linie18 said:
Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4?

Haven't you forgotten to include something?
 
  • #3
whats the answer?
 
  • #4
Any suggestions or answers on this problem yet? I'm having confusion on the same exact problem. I'm trying to search for help for on this problem. It seems to be a confusing one to answer.
 
  • #5


The expressions given above are all related to vector addition, with 1 and 2 representing geometric vector addition and 3 and 4 representing componentwise vector addition. In order for them to define the same vector C_vec, the following conditions need to be true:

1. The length and direction of C_vec must be the same in both pairs of expressions. This means that the magnitude and angle of C_vec must be identical in both cases.

2. The x component of C_vec must be the same in both pairs of expressions. This means that the horizontal component of C_vec must be identical in both cases.

3. The y component of C_vec must be the same in both pairs of expressions. This means that the vertical component of C_vec must be identical in both cases.

Therefore, in order for expressions 1 and 2 to define the same vector as expressions 3 and 4, all of the above conditions must be met. This is because each pair of expressions represents a different aspect of vector addition, and for them to define the same vector, all aspects must match.
 

1. What is the difference between geometric and componentwise vector addition?

Geometric vector addition involves using the head-to-tail method to graphically add two vectors, while componentwise vector addition involves adding the individual components of two vectors to find the resultant vector.

2. Which method is more accurate when adding vectors?

Both methods are equally accurate and can be used depending on the context of the problem. Geometric vector addition is more suitable for visualizing the direction and magnitude of the resultant vector, while componentwise vector addition is more suitable for calculations.

3. Can I use both methods interchangeably?

Yes, both methods can be used interchangeably as they will result in the same resultant vector. However, it is important to understand the concept and context of the problem to determine which method is more appropriate to use.

4. How do I know which method to use?

The method used for vector addition depends on the given information and the desired outcome. If the problem involves finding the resultant vector's direction and magnitude, geometric vector addition would be more suitable. If the problem involves finding the resultant vector's components, componentwise vector addition would be more suitable.

5. Can I use geometric or componentwise vector addition for any number of vectors?

Yes, both methods can be used for adding any number of vectors. However, as the number of vectors increases, the graphical representation of geometric vector addition can become more complex, while componentwise vector addition remains a straightforward calculation.

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