The dot product of vector m with a magnitude of 2 and a direction of 45˚ and vector n with a magnitude of 5 and a direction of 60˚ is given by the formula:
m • n = |m| * |n| * cos(θ)
Where |m| and |n| are the magnitudes of vectors m and n, and θ is the angle between the two vectors.
Plugging in the given values:
|m| = 2
|n| = 5
θ = 60˚ - 45˚ = 15˚
m • n = 2 * 5 * cos(15˚)
m • n = 10 * cos(15˚)
m • n ≈ 9.66
Therefore, the dot product of vector m and vector n is approximately 9.66.