# Thread: Linear Algebra And Matrices. lines

1. ## Linear Algebra And Matrices. lines

I am stuck on the following problems, both from university intro algebra course

Find the parametric equations of the line which intersects each of followinglines orthogonally: x=-9+3t , y=-5+t , z=-3+t and x=-3+2t , y=-7+3t , z=-17+t

Other question

If A is a matric satisfying
-8(A^3)-10(A^2)+8A+I=0
show that A is invertible with
(A^-1)=-1(-8(A^2)-10A+8I)

Im assuming that I is the identity matrix but other than that im lost.

2. Originally Posted by Dani
I am stuck on the following problems, both from university intro algebra course

Find the parametric equations of the line which intersects each of followinglines orthogonally: x=-9+3t , y=-5+t , z=-3+t and x=-3+2t , y=-7+3t , z=-17+t
.
The aligned vector with the first line is,
$\bold{u}=3\bold{i}+\bold{j}+\bold{k}$
The aligned vector with the second line is,
$\bold{v}=2\bold{i}+3\bold{j}+\bold{k}$
To be both orgothonal we need a vector orthogonal to both, for example, the cross product vector,
$\bold{u}\times \bold{v}=\left| \begin{array}{ccc}\bold{i}&\bold{j}&\bold{k}\\3&1& 1\\2&3&1 \end{array} \right|=-2\bold{i}-\bold{k}+7\bold{k}$