Answer to Question #284773 in Physics for Elie

Question

A force 𝐹⃗ = (6𝚤̂ - 𝚥̂) N acts on a particle that undergoes a displacement 𝑑⃗ = (3𝚤̂ + 𝚥̂) m. Find (a) the dot product 𝐹⃗ • 𝑑⃗ and (b) the angle between 𝐹⃗ and 𝑑⃗. 

Answer 1

(a) The dot product:

$$\vec F·\vec d=(6·3)+((-1)·1)=17\text{ J}.$$

(b) The angle:

$$\theta=\arccos\dfrac{\vec F·\vec d}{|\vec F|·|\vec d|}=28°.$$