Calculating Angle between Vector and Plane Normal
Consider the plane given by the equation \(2x – 3y + z – 5 = 0\). Its normal vector is \(\vec{n} = (2, -3, 1)\). Given the vector \(\vec{v} = (4, 1, -2)\), calculate the angle \(\theta\) between \(\vec{v}\) and the plane’s normal vector using the dot product.