Solution to Exercise 3.14.
Trigonometry is a sine of the times.

Exercise 3.14. Use the definition to find the measure of the angle between each pair of lines.
(a)  [–2, 4, –3] and [3, –5, 2].
We compute from the definition of the angle between two lines to obtain

 

 

(b)  The coordinate axes.

The coordinate axes are p[0, 1, 0] and q[1, 0, 0]. Thus, p₁q₁ + p₂q₂ = 0(1) + 1(0) = 0. Hence the measure of the angle between the two coordinate axes is