To find the resultant vector of A + B, one must calculate the horizontal and vertical components of each vector, sum these components to get the resultant vector's components, and then use the Pythagorean theorem and arctan function to find the resultant vector's magnitude and direction.
To find the resultant vector of A + B, where vector A has a magnitude of 122 cm and direction of 145°, and vector B has a magnitude of 110 cm and direction of 270°, we need to break each vector into their horizontal and vertical components and then add them together.
For vector A, the horizontal component (Ax) is 122 cm × cos(145°) and the vertical component (Ay) is 122 cm × sin(145°). For vector B, because it points directly down, the horizontal component (Bx) is 0 and the vertical component (By) is -110 cm (negative because it is in the downward direction). Adding the horizontal components and the vertical components separately, we obtain the resultant vector's components (Rx, Ry).
After calculating the components, we can find the magnitude of the resultant vector using the Pythagorean theorem and determine the direction angle with respect to the horizontal by using the arctan function of Ry/Rx.