Find the direction angle of the vector \(\vec{v} = 2\hat{i} + 3\hat{j}\)

Step 1 ：Step 1: Determine the magnitude of the vector \(\vec{v}\). The magnitude of the vector \(\vec{v}\) can be found using the formula \(|\vec{v}| = \sqrt{x^2 + y^2}\), where \(x\) and \(y\) are the components of the vector. For the vector \(\vec{v} = 2\hat{i} + 3\hat{j}\), the magnitude is \(|\vec{v}| = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}\)

Step 2 ：Step 2: Determine the direction angle of the vector. The direction angle \(\theta\) of a vector can be found using the formula \(\theta = \arctan\left(\frac{y}{x}\right)\), where \(x\) and \(y\) are the components of the vector. For the vector \(\vec{v} = 2\hat{i} + 3\hat{j}\), the direction angle is \(\theta = \arctan\left(\frac{3}{2}\right)\)