11 HL: Vector Equations of Lines in 3D

Complete the following questions before our next class.

Exercise 13A questions 4, 5ac, 6ab

Also, (as a challenge question) can you answer question 2 from class? Both questions are shown below.

  1. Find the vector equation of the line passing through \(A(1,-1,4)\) and \(B(3,3,-1)\).
  2. Find the distance of the point \(A(1,2,3)\) to the line given by
    \[\vec{r}=\begin{bmatrix}4\\2\\1\end{bmatrix}+\lambda \begin{bmatrix}4\\1\\-1\end{bmatrix}\]