Answer: None of the given options is precisely correct. The closest educational intent is (iii), but technically support vectors are data points, not a distance.

Correct definition:
A support vector is a training sample that lies closest to the decision hyperplane and directly influences its position and orientation. For a hard-margin SVM with hyperplane $w^T x + b = 0$:

$w^T x_i + b = \pm 1$ for support vectors, and margin $= 2/||w||$.

• (i) distance between any two data points — false
• (ii) average distance — false
• (iii) distance between any two boundary data points — confuses support vector (a point) with margin (a distance)
• (iv) minimum distance between any two data points — false

If forced to choose: Many university keys mark (iii) as expected answer, interpreting support vectors as the points that define the minimum distance (margin) between classes. Ideally answer should be: "the training vectors closest to the hyperplane that satisfy $y_i(w^T x_i+b)=1$".