State the triangle law of vector addiction

Mathematics

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The triangle law of vector addition states that if two vectors are represented by two sides of a triangle taken in order, then their sum (resultant vector) is represented by the third side of the triangle taken in the opposite order.

Let a⃗\vec{a} and b⃗\vec{b} be two vectors. If a⃗\vec{a} is represented by side AB and b⃗\vec{b} is represented by side BC, then their resultant vector R⃗\vec{R} is represented by side AC.

R⃗=a⃗+b⃗\vec{R} = \vec{a} + \vec{b}

This can be visualized as:

  • Start at point A.
  • Draw vector a⃗\vec{a} from A to B.
  • From point B, draw vector b⃗\vec{b} to point C.
  • The resultant vector R⃗\vec{R} is the vector from A to C.
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