Concepts Of Physics MCQ Edition [Volume 1]PhysicsPhysics and Mathematics
Suppose C = A + B .
Options
- AIt is possible to have | C | < | A | as well as | C | < | B |
- B| C | always equals | A | + | B |
- C| C | never equals | A | + | B |
- D| C | is always larger than | A |
Correct answer
A. It is possible to have | C | < | A | as well as | C | < | B |
Step-by-step solution
Given C = A + B . The magnitude of C is given by | C | = | A |^2 + | B |^2 + 2| A || B | , where is the angle between A and B . If the angle between the vectors is obtuse ( > 90^ ), the term 2| A || B | becomes negative, which can make | C | smaller than both | A | and | B | . For example, if A = 5 i and B = -6 i , then C = - i . Here, | A | = 5 , | B | = 6 , and | C | = 1 . Thus, | C | < | A | and | C | < | B | is possible.