Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Vectors, Exercise 8: EXERCISE 9D

Show that the line through the points with position vectors $9i+2j-5k$ and $i+7j+k$ is parallel to the line $r=\lambda \left(16i-10j-12k\right).$

Find the parametric equations of each of the lines.

$r=2i+13j+k+t\left(i+j-k\right)$

Find the parametric equations of each of the lines.

$r=10j+t\left(2i+5j\right)$

Find the parametric equations of each of the lines.

$r=i-3j+t\left(2i+3j+4k\right)$

Find the parametric equations of the line $L$ through the points$A\left(0, 4, -2\right) and B\left(1, 1, 6\right).$

Hence find the coordinates of the point where the line $L$  crosses the $Oxy$ plane.

The line $L_1$ has vector equation $r=2i-3j+k+\lambda \left(6i+j+3k\right)$ and the line $L_2$ has parametric equations $x=\mu +4, y=\mu -7, z=3\mu .$

Show that $L_1$ and $L_2$ are not parallel.

The line $L_1$ has vector equation $r=2i-3j+k+\lambda \left(6i+j+3k\right)$ and the line $L_2$ has parametric equations $x=\mu +4, y=\mu -7, z=3\mu .$

Find the angle between the line $L_1$ and the line $L_2.$