Question

I was wondering the answer to this question and why the others are wrong.
19. If the magnitude of the sum of two vectors is less than the magnitude of either vector, then
a: the scalar product of the vectors must be negative.
B: the scalar product of the vectors must be positive
c: the vectors must be parallel and in opposite directions
d: The vectors must be parallel and in same directions
e: none of the above

20. If the magnitude of the sum of two vectors is greater than the magnitude of either vector
A: the scalar product of the vectors must be negative B: the scalar product of the vectors must be positive
c: the vectors must be parallel and in opposite directions
d: The vectors must be parallel and in same directions
e: none of the above
THank you!

Answer 1

Solution : 1. Only first part would be right because two vector if are aligned at an angle greater than 90 and smaller than 270 then their scalar product would be negative as well as the magnitude will be less than individual. So go for option A

2. Only part B is correct .the angle between the vector is 0 to 90 either clockwise or anticlockwise in such situation the magnitude of the sum would be greater either of the vectors. If you take them as parallel the answer is also correct but the word they used is must, which is not compulsory because if they are not parallel in the same direction and are aligned at any angle between 0 to 90 degree than magnetised would surely come greather than either of them.