U = ( − 2 , 1 ) u = ( - 2 , 1 ) , v = ( 5 , − 4 ) v = ( 5 , - 4 ) The equation for finding the angle between two vectors θ θ states that the dot product of the two vectors equals the product of the magnitudes of the vectors and the cosine of the angle between them. u ⋅ v = | u | | v | c o s ( θ ) u ⋅ v = | u | | v | c o s ( θ ) Solve the equation for θ θ . θ = a r c ⋅ c o s ( u ⋅ v | u | | v | ) θ = a r c ⋅ c o s ( u ⋅ v | u | | v | ) Find the dot product of the vectors. Tap for more steps... − 14 - 14 Find the magnitude of u u . Tap for more steps... √ 5 5 Find the magnitude of v v . Tap for more steps... √ 41 41 Substitute the values into the equation for the angle between the vectors. θ = arccos ⎛ ⎜ ⎜ ⎝ − 14 ( √ 5 ) ⋅ ( √ 41 ) ⎞ ⎟ ⎟ ⎠ θ = arccos ( - 14 ( 5 ) ⋅ ( 41 ) ) Simplify. Tap for more steps... 2.93049932 2.93049932 u = ( − 2 , 1 ) , v = ( 5 , − 4 ) u = ( - 2 , 1 ) , v = ( 5 , - 4 )
