Question

If v1 = (2,-5) and v2 = (4,-3), then the angle between the two vectors is _________. Round your answer to two decimal places.

Answer 1

The angle between two vectors is given by:
 cos (x) = (v1.v2) / (lv1l * lv2l)
 We have then:
 v1.v2 = (2, -5). (4, -3)
 v1.v2 = (2 * 4) + (-5 * (- 3))
 v1.v2 = 8 + 15
 v1.v2 = 23
 We look for the vector module:
 lv1l = root ((2) ^ 2 + (-5) ^ 2)
 lv1l = 5.385164807
 lv2l = root ((4) ^ 2 + (-3) ^ 2)
 lv2l = 5
 Substituting values:
 cos (x) = (23) / ((5.385164807) * (5))
 x = acos ((23) / ((5.385164807) * (5)))
 x = 31.33 degrees
 Answer:
 The angle between the two vectors is:
 x = 31.33 degrees