# Degree between vector and point

I have a vector and a point $$(x, y)$$. The vector starts from $$(0, 0)$$ and goes to $$(x_1, y_1)$$. $$x$$, $$y$$, $$x_1$$, $$y_1$$ are known. How can I get the degree that vector should rotate clockwise to face this point? Scheme

• Trigonometry; apply it to vector from $(0,0)$ to $(x,y)$ to compute $\text {cos}(\theta)$ and find the angle $\theta$. The same for the other one, finding $\theta_1$. – Mauro ALLEGRANZA Mar 21 at 15:05

You have an another vector $$\vec A$$ which joins $$(0,0)$$ and $$(x,y)$$. So now simply calculate the angle between this factor and your vector using dot product. You have: $$cos \theta = \frac{xx_1+yy_1}{\sqrt{x^2+y^2}\sqrt{x_1^2+y_1^2}}$$ Where $$\theta$$ is angle between the two vectors
• This can be determined on the basis of in which quadrant do $(x,y)$ and $(x_1,y_1)$ lie. So based on their relative position(you will have various cases), you can get the clockwise angle in terms of $\theta$ :) – Tojrah Mar 21 at 17:21