Question

which vector below goes from (0, 0) to (-2, 3)? a. $vec{a}$ b. $vec{d}$ c. $vec{b}$ d. $vec{c}$

Explanation:

Step1: Recall vector definition

A vector from point $(x_1,y_1)$ to $(x_2,y_2)$ has components $(x_2 - x_1,y_2 - y_1)$. Here, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(-2,3)$, so the vector is $(-2 - 0,3 - 0)=(-2,3)$.

Step2: Analyze vector directions on graph

In a coordinate - plane, a vector with $x$ - component negative and $y$ - component positive points to the upper - left.

Answer:

A. $\vec{a}$