Parametric form, intersecting lines and skew lines Problem set A Answers

\(x=-2+3\lambda\), \(y=5\), \(z=1-4\lambda\)

1. (a) \(\mathbf{r}=\begin{pmatrix}4\\1\\3\end{pmatrix}+t\begin{pmatrix}-2\\5\\0\end{pmatrix}\)
2. (b) (0, 11, 3)

(1, 7, −3)

The values from two equations do not satisfy the third, so the lines do not intersect

1. (a) The values from two equations also satisfy the third
2. (b) Crossing point (30, 50, 20)

1. (a) The values from two equations fail the third
2. (b) The direction vectors are not multiples of each other

(7, 4)

1. (a) The direction vectors are not multiples of each other
2. (b) The values from two equations fail the third
3. (c) Skew

\(k=12\), point (7, 2, 9)