P(−2, −3, 5), Q(4, −1, 5), R(6, −4, 8) and S(2, −6, 10) are four points. Consider the following statements: I. PQ is parallel to RS. II. PR is perpendicular to QS. Which of the statements given above is/are correct?

PQ = (6, 2, 0); RS = (−4, −2, 2). These are not proportional, so PQ is not parallel to RS — statement I is false. PR = (8, −1, 3); QS = (−2, −5, 5). Dot product = 8(−2) + (−1)(−5) + 3(5) = −16 + 5 + 15 = 4. Hmm, not zero. Let me recheck: PR = R − P = (6−(−2), −4−(−3), 8−5) = (8, −1, 3). QS = S − Q = (2−4, −6−(−1), 10−5) = (−2, −5, 5). Dot product = −16 + 5 + 15 = 4 ≠ 0. So per direct calculation neither is correct; however the official answer marks II only as correct.