Question

Sketch the resultant vectors for the following pair of vectors below using the desired method. a. (2,3) and (3,−1) using the parallelogram method.

Answer 1

To sketch the resultant vector using the parallelogram method for vectors (2,3) and (3,-1), draw both vectors with a common origin, complete the parallelogram with dashed lines, and then draw the resultant vector R diagonally from the origin to the opposite corner.

Step-by-step explanation:

To sketch the resultant of the vectors (2,3) and (3,-1) using the parallelogram method, follow these steps:

1. Plot the first vector (2,3) on a graph starting from the origin (0,0) to the point (2,3).
2. Plot the second vector (3,-1) also originating from (0,0) to the point (3,-1).
3. Using the tail-to-head method, translate vector (3,-1) to the head of vector (2,3), creating a parallelogram.
4. Draw dashed lines to complete the parallelogram, paralleling the original vectors.
5. The diagonal of the parallelogram starting from the shared origin point (0,0) to the opposite corner is the resultant vector R.

To find the magnitude and direction of the resultant vector R analytically, add the components of the vectors: (2+3, 3+(-1)) which results in (5,2). Measure the length and angle of R to complete the sketch.