# How to find $x$ and $y$ components of a vector if angle between two vectors is Obtuse (greater than 90)?

How to divide $$Q$$ and $$P$$ into its components?
Can you write $$θ$$ in terms of P and Q. if yes then how to write it and from which equation you are calculating the θ?

Assume that the the point of intersection of $$\vec{Q}$$ and $$\vec{P}$$ is the origin of the plane. Because $$\vec{Q}$$ has horizontal component exactly $$-\vec{P}$$ and vertical component exactly $$\vec{R}$$, then $$\vec{Q} = \vec{R}-\vec{P}$$. Since $$\vec{P}$$ has no component in the vertical direction, then it is already divided into horizontal and vertical components.
Then recall that $$\frac{\vec{Q}\cdot\vec{P}}{|\vec{Q}||\vec{P}|}=\cos(\theta)$$ so $$\cos^{-1}\left(\frac{\vec{Q}\cdot\vec{P}}{|\vec{Q}||\vec{P}|}\right)=\theta$$