To calculate v1, v2, and v3 in the circuit, apply Kirchhoff's Current Law (KCL), which states that the sum of currents out of a node equals zero. Begin by writing KCL equations for each node in the circuit. After establishing these equations, solve the simultaneous equations to find the unknown voltages. This method ensures accurate results based on circuit analysis principles. Understanding KCL is essential for solving such circuit problems effectively.