Question

given two vectors with magnitudes of 5 km and 7 km, what are the maximum and minimum possible magnitudes of the resultant vectors?
a 49 km, 35 km
b 12 km, 2 km
c 9 km, 8 km
d 7 km, 5 km

Explanation:

Step1: Recall vector addition rule

For two vectors with magnitudes \( A \) and \( B \), the magnitude of the resultant vector \( R \) satisfies \( |A - B| \leq R \leq A + B \). Here, \( A = 5\space km \), \( B = 7\space km \).

Step2: Calculate maximum magnitude

Maximum magnitude occurs when vectors are in the same direction: \( R_{max}=A + B = 5 + 7 = 12\space km \).

Step3: Calculate minimum magnitude

Minimum magnitude occurs when vectors are in opposite directions: \( R_{min}=|A - B| = |5 - 7| = 2\space km \).

Answer:

12 km, 2 km (corresponding to option B)