Explanation of straight line and plane equations in space. Parameterized equation of a straight line in three dimensions is given as \( \mathbf{r}(t) = \mathbf{r_0} + t \mathbf{v} \) where \( \mathbf{r}(t) \) is the vector at any point on the line, \( \mathbf{r_0} \) is the vector from a fixed point on the line, \( \mathbf{v} \) is the directing vector, and \( t \) is the parameter