Question

When a vector of magnitude 10 units is added to a vector of magnitude 5 units, the magnitude of the resultant vector will be:

• A. Exactly 5 units
• B. Exactly 10 units
• C. Exactly 15 units
• D. 0 units, 10 units, or some value between them
• E. 5 units, 15 units, or some value between them

Answer 1

Answer: (E)

5 units, 15 units, or some value between them

Given : $|A_1|=10$ units $|A_2|=5$ units

Maximum magnitude of resultant vector, $A_{max}=|A_1|+|A_2|=10+5=15$ units

Minimum magnitude of resultant vector, $A_{min}=|A_1-A_2|=10-5=5$ units

$\therefore$ Range of magnitude of resultant vector: $5\le A_R\le 15$ units