The vector that represents the family of vectors, including that between the points (3, - 1) and (- 3, - 4) is equal to <6, 3>. (Correct choice: D)
How to find the component form of a vector
According to linear algebra, the definition of a vector in component form, that is, in rectangular form, is equal to the difference between the coordinates of the two ends, the final one with respect to the initial one. That is:
v = (Δx, Δy)
Where Δx and Δy are the changes of the vector parallel to each of the two orthogonal axes.
Each end can be represented as a vector whose initial end is at the origin, then:
v = (3, - 1) - (- 3, - 4)
v = (3 + 3, - 1 + 4)
v = <6, 3>
The vector that represents the family of vectors, including that between the points (3, - 1) and (- 3, - 4) is equal to <6, 3>. (Correct choice: D)
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