Question

For a line passing through a point with position vector \[\vec{a}\] and parallel to a vector \[\vec{b}\], which is the vector equation?

Options

• \[\vec{r}=\lambda\vec{a}\vec{b}\]

• \[\vec{r}=\vec{a}\lambda+\vec{b}\]

• \[\vec{r}=\vec{a}+\lambda\vec{b}\]

• \[\vec{r}=\vec{b}+\lambda\vec{a}\]

Answer 1

The position vector \[\vec{a}\] locates a point on the line. Adding \[\lambda\vec{b}\] produces the position vector \[\vec{r}\] of any point on the line.