Calculating Structural Angle using Dot Product

00:00 4 marks

  • Build Confidence
  • HL
  • Tier 4
  • Dot product
  • Angle Calculation
  • Inverse trigonometric functions
  • Vector norms

In a structural analysis of a building frame, two beams are modeled by the vectors \(\vec{A} = \langle 1, 2 \rangle\) and \(\vec{B} = \langle 2, 1 \rangle\). Using the scalar (dot) product, determine the acute angle between these two beams in degrees.

Hint Hint

Hint

Recall that the dot product is given by \(\vec{A} \cdot \vec{B} = ||\vec{A}|| ||\vec{B}|| \cos\theta\). Solve for \(\theta\) using the inverse cosine.

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Complete Answer

\(\theta = \arccos\left(\frac{4}{5}\right) \approx 36.87^\circ\)

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