Magnitude of Vector C in Physics

What is the magnitude of Vector C based on the given vectors A and B?

Given: Vector A: [tex]$$\vec{A} = 4.6\hat{x} + 3.8\hat{y}$$[/tex], Vector B: [tex]$$\vec{B} = -6.8\hat{x} - 6.8\hat{y}$$[/tex], and Vector A + Vector B + Vector C = 0. Calculate the magnitude of Vector C in metres to two decimal places.

Answer:

The magnitude of Vector C is 3.72 m.

Given the vectors A and B, we can calculate the magnitude of Vector C by first adding vectors A and B together. This will give us the resultant vector.

By adding vectors A and B, we get: [tex]$$\vec{A} + \vec{B} = -2.2\hat{x} - 3.0\hat{y}$$[/tex]

Since the sum of vectors A, B, and C is zero, we can infer that Vector C has the same magnitude as the resultant vector of A + B but in the opposite direction. Therefore, Vector C has a magnitude of 3.72 m.

The magnitude of Vector C can be calculated using the formula |$\vec{C}$| = |$\vec{A} + \vec{B}$|, which results in: [tex]$$\sqrt{(-2.2)^2 + (-3.0)^2} = \sqrt{13.84} = 3.72 \text{ m (to 2 decimal places)}$$[/tex]

Therefore, the magnitude of Vector C is 3.72 metres based on the given vectors A and B.