if |A|=2, |B| =4, |C| =5, find the vector sum a+b+c in ordered pair notation, also find the angle theta
To find the vector sum \(\mathbf{a} + \mathbf{b} + \mathbf{c}\), we can perform the vector addition component-wise. Given that \(|\mathbf{A}| = 2\), \(|\mathbf{B}| = 4\), and \(|\mathbf{C}| = 5\), we can find the corresponding vectors as follows:
\(|\mathbf{A}| = \sqrt{A_x^2 + A_y^2} = 2\)
\(|\mathbf{B}| = \sqrt{B_x^2 + B_y^2} = 4\)
\(|\mathbf{C}| = \sqrt{C_x^2 + C_y^2} = 5\)
To find the vector sum, we need to find the components \(A_x, A_y, B_x, B_y, C_x,\) and \(C_y\). However, we don't have enough information to determine these values from the given magnitudes alone. We need additional information such as angles or specific coordinates for each vector.
Similarly, to find the angle \(\theta\) between the vectors, we need information about the vector components. Without any additional details, we cannot calculate the angle.