Solving Vector Equations: F + G + __ = 0

[looklikeaflip]

Vector F has magnitude of 9. Vector G has magnitude of 2. which of the following vectors could possibly satisfy the vector equation F+G+__=0

The possibilities are listed with drawn vectors with no degrees, just vectors in space.

The magnitude possibilities are 5, 2, 8, 6, 12.

The answer is 8 with the vector drawn to the left and slightly in the y direction.

I tried solving the problem but it seems impossible without directions included.

I also tried making a right triangle out of all the vectors because the addition of them are 0.

Is my reasoning incorrect?

 

[anathema]

Your reasoning is not incorrect, but there are a few things that could be clarified. Let's break down the problem step by step:

1. The forum post states that the vectors F and G have magnitudes of 9 and 2, respectively. This means that the lengths of these vectors are 9 units and 2 units, but we do not know their directions yet.

2. The forum post then asks which vector could possibly satisfy the equation F+G+__=0. This means that we need to find a third vector that, when added to F and G, will result in a total of 0 units in both magnitude and direction.

3. The magnitude possibilities listed are 5, 2, 8, 6, and 12. These are the possible lengths for the third vector that we need to find. However, we cannot simply choose any one of these magnitudes and draw a vector with that length. We also need to consider the direction of the vector.

4. Since we know that F+G+__=0, we can rearrange the equation to solve for the missing vector. This gives us the equation F+G= -__. This means that the third vector must have the same magnitude as F+G, but in the opposite direction.

5. Now, we can use the Pythagorean theorem to find the magnitude of F+G. This will give us the length of the third vector that we need to find. The Pythagorean theorem states that the square of the hypotenuse (in this case, the magnitude of F+G) is equal to the sum of the squares of the other two sides (in this case, the magnitudes of F and G). So, we have (F+G)^2 = F^2 + G^2. Plugging in the given magnitudes, we have (9+2)^2 = 9^2 + 2^2, which simplifies to 121 = 85. This means that the magnitude of F+G is √85.

6. Now that we know the magnitude of F+G, we can use this to find the magnitude of the missing vector. Since we know that the missing vector must have the same magnitude as F+G, but in the opposite direction, we can use the same Pythagorean theorem equation to solve for this missing magnitude. So, we have (__)^2 = (F+G