The question is missing the alternatives. Here is the complete question.
Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:
A. 2 units
B. 5 units
C. 8 units
D. 12 units
Answer: A. 2 units
Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.
In this question, the vectors have magnitude and angle varies from 0° to 180°.
When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:
![V_{R}=8+5](https://tex.z-dn.net/?f=V_%7BR%7D%3D8%2B5)
= 13
When the angle is 180°, it means vectors are in opposing directions, so:
![V_{R} = |A| - |B|](https://tex.z-dn.net/?f=V_%7BR%7D%20%3D%20%7CA%7C%20-%20%7CB%7C)
![V_{R} = 8-5](https://tex.z-dn.net/?f=V_%7BR%7D%20%3D%208-5)
= 3
From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.
<u>The least value is 3, so it </u><u>cannot</u><u> have a value of </u><u>2 units</u><u>.</u>