बिंदु (2, 5, -3) की समतल सदिश समीकरण r · (6i - 3j + 2k) = 6 से लंबवत दूरी ज्ञात कीजिए।

The value of λ for which the angle between lines r = i + j + k + p(2i + j + 2k) and r = (1 + q)i + (1 + qλ)j + (1 + q)k is π2:

Match the mathematical operations in List-I with their corresponding correct values in List-II: List–I: (A) The angle between vectors a = i + 2j + k and b = 2i - j + 2k is (B) The scalar projection of vector a = 3i + 4j on vector b = i + 2j is (C) The shortest distance between lines (x - 1)/2 = (y + 1)/(-1) = z/3 and (x + 2)/(-1) = (y - 3)/2 = (z - 1)/1 is (D) The equation of the plane passing through point (1, 2, 3) and perpendicular to vector n = 2i - j + k is List–II: (p) cos-1(3/√30) (q) 11/√5 (r) 7/√14 (s) 2x - y + z = 5 (t) 9/√14