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📐 Mathematics  ·  Vector Algebra  ·  JEE

If a.b = a.c and a is non-zero, it necessarily means:

Answer: a is perpendicular to (b - c).

  • A b = c necessarily, in this particular case
  • B a is parallel to vector b specifically
  • C b - c = 0, meaning b and c are equal
  • D a is perpendicular to (b - c)

Correct answer: D. a is perpendicular to (b - c)

Explanation: a.b = a.c means a.(b-c) = 0. So a is perpendicular to (b-c). This does NOT mean b = c.

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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