The magnitude of the sum of two vectors A and B, |A+B| is equal to |A| + |B|

Question

Choices:

A. Vectors A and B are perpendicular.

B. Vectors A and B are in opposite directions.

C. Vectors A and B are in the same direction.

 

What's the correct answer between them, and why not the other ones?

Answer 1

Vectors A and B are in the same direction.  The correct answer is (C).

 

(A) is wrong because if they were perpendicular, the magnitude of the sum would be √(|A|² + |B|²).

 

(B) is wrong because if they were in opposite directions, the magnitude of the sum would be ||A| - |B||.