GATE AG 2008 • Q6 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Scalar and vector point functions

Question Statement:

The cross product of x⃗ = 2i + j and y⃗ = i − 2j + k is

Options:

  • (A) i − j + 2k
  • (B) i − 2j + 5k
  • (C) i − 2j − 5k
  • (D) 2i − 4j

Official Answer Key:

C

Step-by-Step Solution & Explanation

x⃗×y⃗ = |i j k; 2 1 0; 1 −2 1| = i(1×1 − 0×(−2)) − j(2×1 − 0×1) + k(2×(−2) − 1×1) = i(1) − j(2) + k(−5) = i − 2j − 5k.

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