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📐 Mathematics  ·  Vector Algebra  ·  JEE

If a x b = a x c (a is non-zero), then necessarily:

Answer: b - c is parallel to a.

  • A b = c
  • B b - c is perpendicular to a
  • C b - c is parallel to a
  • D b + c = 0

Correct answer: C. b - c is parallel to a

Explanation: a×b = a×c → a×(b−c) = 0. Cross product is zero iff vectors are parallel (or one is zero). So (b−c) is parallel to a. Note: b−c need not be zero, so b≠c in general. Answer: b−c is parallel to a.

xya (4,1)b (2,3)a + b (6,4)

Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.

Concept context

Vectors, dot product, cross product, and geometric applications

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