Question

When a vector of magnitude 12 units is added to a vector of magnitude 8 units, the magnitude of the resultant vector will be:

• A. exactly 4 units
• B. exactly 20 unit
• C. exactly 2 unit
• D. 0 units, 10 units, or some value between them
• E. 4 units, 20 units, or some value between them

Answer 1

The correct option is E 4 units, 20 units, or some value between them

Given : $|A|=12$ units $|B|=8$ units

Maximum magnitude of resultant vector, $R_{max}=|A|+|B|=12+8=20$ units

Minimum magnitude of resultant vector, $R_{min}=|A-B|=|12-8|=4$ units

Thus range of magnitude of resultant vector: $4\le R\le 20$ units