GATE AG 2011 • Q28
MCQ • 1 Mark
Section 1: Engineering Mathematics
Calculus
Subtopic: Limit, continuity and differentiability
Question Statement:
A plane contains the following three points: P(2,1,5), Q(−1,3,4) and R(3,0,6). The vector perpendicular to the above plane can be represented as
Options:
-
(A) 2i − j + k
-
(B) i + 2j + 2k
-
(C) 2i + 3j + k
-
(D) i + 2j + k
Step-by-Step Solution & Explanation
Form two vectors in the plane: PQ = Q−P = (−3,2,−1) and PR = R−P = (1,−1,1). The normal to the plane is PQ × PR = |i j k; −3 2 −1; 1 −1 1| = i(2·1 − (−1)(−1)) − j((−3)(1) − (−1)(1)) + k((−3)(−1) − 2·1) = i(2−1) − j(−3+1) + k(3−2) = i(1) − j(−2) + k(1) = i + 2j + k, matching option (D) exactly.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test