that do not cross at right angles is the same as the angle determined by vectors normal to the lines or by the vectors parallel to the lines.

Use this fact and the results of Exercise 31 or 32 to find the acute angles between the lines.

y = √3x - 1, y = -√3x + 2

Exercise 31

Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the vector v is the negative reciprocal of the slope of the given line.

Exercise 32

Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope of the line segment representing v is the same as the slope of the given line.

0 X 0 2 11 L2 L1 V2. 0 L2 -L