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Order the steps: angle between two lines from direction ratios

Exercise and reference answers

Steps
  1. Read off the direction ratios of both lines
  2. Multiply matching components and add them up
  3. Divide by the magnitude of each direction-ratio triple
  4. Take the modulus so the angle comes out acute
  5. Apply cos⁻¹ to get θ

Explanation

The route your syllabus gives: dot the ratios, divide by both magnitudes, take the modulus for the acute angle then invert the cosine. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.
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