Question

When using the associative law to add three vectors, what remains constant regardless of how you group them?

Options

• Only magnitude of the resultant

• Only direction of the resultant

• Both the magnitude and direction of the final resultant

• Neither the magnitude nor the direction

Answer 1

Both the magnitude and direction of the final resultant

Explantion:

The associative law states that \[(\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C})\]. Both grouping methods produce the same final resultant with identical magnitude and direction, proving that the final result is independent of how the vectors are grouped.