Question

which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest? view available hint(s) a and f a and e d and b c and d e and f submit

Explanation:

Step1: Recall vector subtraction property

The magnitude of $\vec{u}-\vec{v}$ is related to the magnitudes of $\vec{u}$ and $\vec{v}$ and the angle between them. Geometrically, vector - subtraction $\vec{u}-\vec{v}=\vec{u}+(-\vec{v})$. The magnitude of the resultant vector $|\vec{u}-\vec{v}|=\sqrt{|\vec{u}|^{2}+|\vec{v}|^{2}-2|\vec{u}||\vec{v}|\cos\theta}$, where $\theta$ is the angle between $\vec{u}$ and $\vec{v}$. The larger the magnitudes of the two vectors and the closer the angle between them to $180^{\circ}$, the larger the magnitude of the difference vector.

Step2: Analyze each option

• For option A and F: Vectors A and F have relatively large magnitudes and are almost in opposite directions.
• For option A and E: Vector E has a relatively small magnitude compared to A, so $|\vec{A}-\vec{E}|$ will not be as large as some other combinations.
• For option D and B: The magnitudes of D and B are not as large as A and F, and the angle between them is not as close to $180^{\circ}$ as A and F.
• For option C and D: The magnitudes of C and D are not as large as A and F, and the angle between them is not optimal for a large - magnitude difference vector.
• For option E and F: Vector E has a small magnitude, so $|\vec{E}-\vec{F}|$ will not be the largest.

Answer:

A. A and F