Final answer:
Using the Pythagorean theorem, the magnitude of the resultant vector for vectors A (5 units west) and B (3 units south) is the square root of 34 units.
Step-by-step explanation:
The question involves the concept of vector addition and how to calculate the resultant vector's magnitude using the magnitudes and directions of the initial vectors. For vector A, with a magnitude of 5 units pointing west, and vector B, with a magnitude of 3 units pointing south, we can use the Pythagorean theorem to find the magnitude of the resultant vector. Since these vectors are perpendicular to each other, the resultant vector (let's call it R) is the hypotenuse of a right-angled triangle, with the other two sides being the magnitudes of vectors A and B.
To compute the magnitude of R, we apply the Pythagorean theorem:
R = √(A² + B²)
Substitute the given values:
R = √(5² + 3²)
R = √(25 + 9)
R = √34
Hence, the magnitude of the resultant vector is √34 units.