The conversation between human and AI assistant.
At what angle should the two vector 2F and√2F act so that the resultant force is F√10?
Can you walk me through the calculation?
Sure. Let's call the angle between the two vectors θ. 
The dot product of the two vectors 2F and √2F is (2F)(√2F)cosθ. 
The magnitude of vector 2F is 2F, and the magnitude of vector √2F is √2F. 
Therefore, we can plug in the values to get: cosθ = (2F)(√2F) / (2F)(√2F) = 1/√2 
To solve for θ, we take the inverse cosine of both sides: θ = cos⁻¹(1/√2) ≈ 45°