How is this relevant to solving the problem? Just because you can combine two numbers given in the problem to produce a third doesn't mean you should do it. You need to have a valid reason for doing so.Ineedhelpwithphysics said:
Vector addition is the process of combining two or more vectors to produce a resultant vector. This involves adding the corresponding components of the vectors, often using geometric or algebraic methods.
To find the angle between two vectors, you can use the dot product formula: \( \mathbf{A} \cdot \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos(\theta) \). Rearrange this to solve for the angle \( \theta \): \( \theta = \cos^{-1} \left( \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} \right) \).
The resultant vector is the vector obtained by adding two or more vectors. It represents the combined effect of the original vectors. For vectors \( \mathbf{A} \) and \( \mathbf{B} \), the resultant vector \( \mathbf{R} \) is \( \mathbf{R} = \mathbf{A} + \mathbf{B} \).
Geometrically, vectors are added using the tip-to-tail method. Place the tail of the second vector at the tip of the first vector. The resultant vector is drawn from the tail of the first vector to the tip of the second vector. This can also be visualized using the parallelogram method.
To add vectors using components, break each vector into its horizontal (x) and vertical (y) components. Add the corresponding components separately: \( \mathbf{R}_x = \mathbf{A}_x + \mathbf{B}_x \) and \( \mathbf{R}_y = \mathbf{A}_y + \mathbf{B}_y \). The resultant vector \( \mathbf{R} \) can then be found using \( \mathbf{R} = \sqrt{\mathbf{R}_x^2 + \mathbf{R}_y^2} \) and the angle \( \theta \) using \( \theta = \tan^{-1} \left( \frac{\mathbf{R}_y}{\mathbf{R}_x} \right) \).