Question

What is the angle between force F=3i+4j-5k unit and displacement S=4j-3k unit?

Answer 1

Explanation:

For angle between two vectors use

_ _

F.s = |F| |s| cosx

where cosx is angle between both vectors

_ _

cosx=F . s

|F| |s|

$\cos(x) = \frac{(3i + 4j - 5k).(0i + 4j - 3k)}{ \sqrt{ {3}^{2} + {4}^{2} + { - 5}^{2} } \times \sqrt{ {4}^{2} + { - 3}^{2} } } \\ \cos(x) = \frac{0 + 16 + 15}{5 \sqrt{2 } + 5} \\ \cos(x ) = \frac{31}{5 (\sqrt{2} + 1)}$