Precalculus Question of the Day

1. The vector from the tip of $\vec v$ to the tip of $\vec w$.
2. The vector from the tail of $\vec v$ to the tail of $\vec w$.
3. The vector from the tip of $\vec w$ to the tip of $\vec v$. (correct answer)
4. The vector from the tip of $\vec v$ to the tail of $\vec w$.

Explanation: This question tests understanding of vector subtraction and how to represent it graphically using the tip-to-tip method. Graphically, when vectors v and w are drawn from the same initial point (tail-to-tail), the vector v - w is represented by the vector from the tip of w to the tip of v, forming a triangle. To find v - w graphically, we can rewrite it as v + (-w): first draw v, then draw -w (the opposite of w), place the tail of -w at the head of v, and the resultant from the tail of v to the head of -w is v - w. Choice C is correct because it properly describes the tip-to-tip method, going from the tip of w to the tip of v. Choice A describes the graphical vector going from the tip of v to the tip of w, but v - w goes from the tip of w to the tip of v (the opposite direction). For the tip-to-tip graphical method, place both vectors tail-to-tail and draw the difference vector from the tip of what you're subtracting (w) to the tip of what you're subtracting from (v).