Question

Find the angle between the given vectors to the nearest tenth of a degree. u = (8, 4), v = (9, -9)

Answer 1

Answer:

71.6 degrees

Step-by-step explanation:

The formula for calculating the angle between two vectors is expressed as;

u.v = |u||v|cos theta

u.v = (8, 4).(9, -9)

u.v = 8(9)+4(-9)

u.v = 72-36

u.v = 36

|u| = √8²+4²

|u| = √64+16

|u| = √80

|v| = √9²+(-9)²

|v| = √81+81

|v| = √162

36 = √80*√162 cos theta

36 = √12960 cos theta

36 = 113.84 cos theta

cos theta = 36/113.84

cos theta = 36/113.84

cos theta = 0.3162

theta = arccos (0.3162)

theta = 71.6 degrees

Hence the angle between the given vectors is 71.6 degrees

Answer 2

Answer:

71.6°

Step-by-step explanation:

arctan(4/8) - arctan(-9/9) = 26.57° - (-45°) ≈ 71.6°