Question

Find a.b given that A= 3m and B = 5m at an angle of 45°

Answer 1

By definition, the dot product is given as follows:

$$\mathbf{a}\cdot\mathbf{b} = AB\cos \theta$$

where $\theta = 45\degree$. Thus, obtain:

$$\mathbf{a}\cdot\mathbf{b} = 3m\cdot 5m\cdot \cos 45\degree = 15m^2\cdot \dfrac{\sqrt{2}}{2} = 7.5\sqrt2m^2\approx 11m^2$$

Answer. $7.5\sqrt2m^2\approx 11m^2$.