Question 1189173
<pre>
The line l<sub>1</sub> has eq:

{{{r}}}{{{""=""}}}{{{(matrix(3,1,3,1,2))}}}{{{""+""}}}{{{t*(matrix(3,1,-1,3,2))}}}

(a)  the point A(-8,34,n) lies on l<sub>1</sub>, find the value of n.

{{{r}}}{{{""=""}}}{{{(matrix(3,1,x,y,z))}}}{{{""=""}}}{{{(matrix(3,1,3,1,2))}}}{{{""+""}}}{{{t*(matrix(3,1,-1,3,2))}}}

We substitute A for < x,y,z >

{{{(matrix(3,1,-8,34,n))}}}{{{""=""}}}{{{(matrix(3,1,3,1,2))}}}{{{""+""}}}{{{t*(matrix(3,1,-1,3,2))}}}    {{{system(-8=3-t,34=1+3t,n=2+2t)}}}

Both the first and second equations give t=11, 
substitute t=11 in the 3rd equation and get n=24.

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(b) The line {{{r}}}{{{""=""}}}{{{(matrix(3,1,1,-2,u))}}}{{{""+""}}}{{{s*(matrix(3,1,-1,p,q))}}}

intersects l<sub>1</sub> at A and is perpendicular to l<sub>1</sub>.

We know this second line also goes through A, so we substitute A

{{{(matrix(3,1,-8,34,24))}}}{{{""=""}}}{{{(matrix(3,1,1,-2,u))}}}{{{""+""}}}{{{s*(matrix(3,1,-1,p,q))}}}

I'm tired.  Maybe I'll finish later.  You have to make sure the dot product is zero.


Edwin</pre>