Three vectors are shown in Fig. 3-32 (A = 62.0 , B = 58.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors.
(a) Give the resultant in terms of components.
Rx =
Ry =
(b) What is the magnitude of the resultant?
What is the resultant's angle above the +x axis?
To determine the sum of the three vectors, we need to add them together using vector addition. Let's denote the three vectors as A, B, and C.
(a) The first step is to find the components of each vector. We'll break down each vector into its x and y components.
For vector A, the magnitude is given as 62.0. However, we need to find its x and y components. To do this, we use the magnitude and the angle it makes with the x-axis. Since no angle is provided for vector A, we assume it is aligned with the x-axis, which means the angle is 0 degrees. Therefore, the x component of A is 62.0 * cos(0) = 62.0, and the y component is 62.0 * sin(0) = 0.
For vector B, the magnitude is given as 58.0, and the angle it makes with the x-axis is 58.0°. To find the x and y components, we use the magnitude and the angle. The x component of B is 58.0 * cos(58.0°), and the y component is 58.0 * sin(58.0°). Calculate these values to get the x and y components of B.
Next, we need to find the components for vector C. Unfortunately, the question does not provide any information about vector C. Therefore, we cannot determine its x and y components. Without this information, it is not possible to find the sum of the three vectors accurately.
(b) Since we don't have the necessary information to find the components of vector C, we cannot determine the magnitude and angle of the resultant. We can only find the sum of the two vectors A and B, but not C.