Angle Between Intersecting Lines in 3D

00:00 3 marks

  • Exam Style - Paper 2
  • SL & HL
  • Tier 2
  • Vectors
  • Dot product
  • Angle between Vectors
  • Magnitude of vectors
  • Acute Angle

Two lines in 3D space have direction vectors \(\mathbf{a} = \begin{pmatrix} 1 \\ 2 \\ -1 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 2 \\ -1 \\ 3 \end{pmatrix}\). Find the acute angle between these two lines. Give your answer in degrees to one decimal place.

Hint Hint

Hint

Use the dot product formula \(\cos \theta = \frac{\mathbf{a} \cdot \mathbf{b}}{\|\mathbf{a}\| \|\mathbf{b}\|}\) to find the angle. Remember to find the acute angle.

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Complete Answer

\(\theta = 70.9^\circ\)

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