Resultant Vector Homework: Min Value of |A+B+C|

In summary, the three vectors A, B, and C have magnitudes A=5, B=6, and C=7 and can form the sides of a triangle. Therefore, the minimum value of |A+B+C| is zero.
  • #1

Homework Statement

Three vectors A, B, C have magnitudes A=5, B=6 and C=7.
The minimum value of |A+B+C| is
*A represents magnitude, A represents the vector (magnitude and direction)

Homework Equations

The Attempt at a Solution

I got 4 because I think that the maximum possible cancellation occurring would be 7-(6+5). But it's wrong.
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  • #2
Im not sure exactly how to approach this, i have a guess, but ill have to work on it. I am off to bed now, though. An example. Let the magnitude 6 vector point at 120 degrees. Let the 5 magnitude vector point at 60 degrees. Let the 7 vector point directly down. Whats the magnitude? Can you mathematically find a relationship between the vector components and their magnitudes?
  • #3
I just figured it out, but thanks anyway. The three vectors can form the sides of a triangle, so the minimum will be zero.
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1. What is a resultant vector?

A resultant vector is a single vector that represents the combined effect of two or more individual vectors. It is the sum of all the individual vectors and can be calculated using vector addition.

2. What is the significance of finding the minimum value of |A+B+C|?

The minimum value of |A+B+C| indicates the shortest possible distance between the initial and final points of the resultant vector. This is useful in many applications, such as navigation and engineering, where finding the most efficient or direct path is important.

3. How is vector addition used to calculate the resultant vector?

Vector addition involves breaking down each vector into its horizontal and vertical components, adding the corresponding components together, and then using the Pythagorean theorem to calculate the magnitude of the resultant vector. The direction of the resultant vector can also be determined using trigonometric functions.

4. Can the minimum value of |A+B+C| be negative?

No, the minimum value of |A+B+C| cannot be negative. The magnitude of a vector is always positive, and the minimum value is the smallest possible value, which cannot be negative.

5. What factors can affect the minimum value of |A+B+C|?

The minimum value of |A+B+C| can be affected by the magnitudes and directions of the individual vectors, as well as their spatial relationship to each other. Changing any of these factors can result in a different minimum value for the resultant vector.

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