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📐 Mathematics  ·  Vector Algebra  ·  JEE

In the reciprocal system, if a<sub>prime</sub> = (b x c)/[abc], then a . a<sub>prime</sub> =

Answer: 1.

  • A 0
  • B [a b c]
  • C a x b
  • D 1

Correct answer: D. 1

Explanation: By definition of reciprocal vectors: a.a<sub>prime</sub> = 1, a.b<sub>prime</sub> = 0, a.c<sub>prime</sub> = 0. The reciprocal system is the dual basis.

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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