Final answer:
The resultant vector A + B has a magnitude of S√1.5 and points to the left and upward, not matching any of the provided options. Vector A's components are derived from its angle with the positive x-axis, and vector B is entirely along the negative x-axis. The resultant vector's magnitude is found using the Pythagorean theorem.Therefore, none of the options given (a, b, c, d) correctly describe the magnitude.
Step-by-step explanation:
The question involves the addition of two vectors, vector A and vector B, both having magnitudes of S units. Vector A makes a 45° angle with the positive x-axis, while vector B is directed along the negative x-axis. To find the resultant vector A + B, we can decompose vector A into its x and y components. The x component of vector A is Ax = Scos(45°) = S/√2, and the y component is Ay = Ssin(45°) = S/√2. Vector B only has an x component, Bx = -S, since it is directed along the negative x-axis with no y component.
Adding the components, we get (A + B)x = Ax + Bx = S/√2 - S. Since S/√2 is less than S, the x component of the resultant vector will be negative, pointing to the left. The y component of the resultant vector is just Ay = S/√2. To find the magnitude of vector A + B, we use the Pythagorean theorem: |A + B| = √[(S/√2 - S)² + (S/√2)²]. Simplifying yields |A + B| = S√[½ + 1] = S√(3/2) = S√1.5, which is less than 2S but more than S.
Therefore, none of the options given (a, b, c, d) correctly describe the magnitude. For direction, the resultant vector is pointing left due to the negative x component and slightly up due to the positive y component.