What is the magnitude of the vector sum of the four vectors

In summary, the conversation is about four vectors with a magnitude of 62 m lying along the sides of a parallelogram, with an angle of 49 degrees between vector A and B. The question is asking for the magnitude of the vector sum of the four vectors, which can be found by finding the magnitude of the diagonal of the parallelogram. However, the addition or cancellation of vectors depends on their direction and positioning. The figure is necessary to determine the exact magnitude.
  • #1
AraProdieur
27
0
Four vectors, each of magnitude 62 m, lie along the sides of a parallelogram as shown in the figure. The angle between vector A and B is 49 degrees.
What is the magnitude of the vector sum of the four vectors? Answer in units of m.

So far, I have drawn the picture and made out with a parallelogram with the left side as vector A, the top vector C, the right vector D, and the bottom vector B with all of the sides congruent to each other respective to 62 m, and also the angle with between vector A and B is 49 degrees which also means that between C and D is the same while between both A and C and B and D is 131 degrees in between.

What I've been thinking was since I have to find the magnitude of the vector sum of the four vectors, wouldn't it be the same as finding the magnitude diagonal of the parallelogram? or am I off the tee here?
 
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  • #2
Can you post a link to the figure, or uplink it as an attachment? We'd like to help, but we need the figure. Thanks.
 
  • #3
If A and C point in the same direction (parallel), they are additive, otherwise if anti-parallel they cancel. Similarly for B and D.

If the head (point) of A touches the tail of B, then they are additive, and resultant is the diagonal. If the point of B touches the tail of C, then C is in the opposite direction of A, and their contributions to the vector sum cancel.
 

What is the magnitude of the vector sum of the four vectors?

The magnitude of a vector sum is the length of the resulting vector when multiple vectors are added together. It is calculated using the Pythagorean theorem, where the square of the magnitude is equal to the sum of the squares of the individual vector components.

Are all four vectors required to calculate the magnitude of the vector sum?

Yes, the magnitude of the vector sum is dependent on all four vectors being present. Each vector contributes to the overall direction and magnitude of the resulting vector.

Does the order of the vectors matter when calculating the magnitude of the vector sum?

No, the order in which the vectors are added does not affect the magnitude of the resulting vector. However, the direction of the resulting vector may be different depending on the order of addition.

What is the difference between the magnitude of the vector sum and the scalar sum of the four vectors?

The magnitude of the vector sum takes into account the direction of the vectors, while the scalar sum only considers the numerical values of the vectors. The scalar sum is simply the sum of the magnitudes of each individual vector.

Can the magnitude of the vector sum be negative?

No, the magnitude of a vector is always a positive value. It represents the distance or length of the vector and cannot be negative.

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