1. Let's state the problem: You want to find the intersection point of two vectors (or lines) without using a parameter like $\lambda$. 2. Typically, vector intersection problems involve finding a common point that satisfies both vector equations. 3. Instead of using parameters, you can set the vector components equal to each other and solve the resulting system of equations. 4. For example, if you have two vectors represented as points or parametric forms: $$\vec{r_1} = (x_1, y_1, z_1)$$ $$\vec{r_2} = (x_2, y_2, z_2)$$ 5. To find their intersection, set the components equal: $$x_1 = x_2$$ $$y_1 = y_2$$ $$z_1 = z_2$$ 6. Solve this system of equations directly for the coordinates of the intersection point. 7. This method avoids introducing parameters like $\lambda$ and focuses on solving the system of equations derived from the vector components. 8. If the system has a solution, that solution is the intersection point. 9. If no solution exists, the vectors (or lines) do not intersect. This approach is straightforward and uses basic algebra to find the intersection point without parameters.