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The parallelogram law of vector addition: |a + b|<sup>2</sup> + |a - b|<sup>2</sup> =

Answer: 2(|a| 2 + |b| 2 ).

  • A 2|a|<sup>2</sup>
  • B 2|b|<sup>2</sup>
  • C 2(|a|<sup>2</sup> + |b|<sup>2</sup>)
  • D 4(|a|<sup>2</sup> + |b|<sup>2</sup>)

Correct answer: C. 2(|a|<sup>2</sup> + |b|<sup>2</sup>)

Explanation: Parallelogram law of cosines: |a+b|<sup>2</sup> + |a-b|<sup>2</sup> = 2(|a|<sup>2</sup> + |b|<sup>2</sup>). The sum of squares of diagonals equals twice the sum of squares of the sides.

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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