Final answer:
The analytical method allows us to determine the magnitude and direction of resultant vectors using the Pythagorean theorem and trigonometric identities.
Step-by-step explanation:
The analytical method of determining the magnitude and direction of a resultant vector involves using the Pythagorean theorem and trigonometric identities. In this method, we break down vectors into their x and y components and then use these components to find the magnitude and direction of the resultant vector.
In the given figure, since AB=1.8 and AC=1.44in, we can use trigonometry to find the x and y components of the vectors AB and AC based on the given angle of AB which is 128°. Then, we can use the Pythagorean theorem and trigonometric identities to find the magnitude and direction of the resultant vector.