# Orthogonal vector equation (Ax=b)

1. May 27, 2013

### jt16733

Hi

I'm having problems understanding vector representation in the form Ax=B could someone please point me in the right direction

A vector equation for a given straight line is r = (i + 3j) + t(-i-j).
i) Show that the point (1,2) does not lie on this line.
ii) Construct a vector equation for the line that does go through the point (1;2), and is
perpendicular to r.
iii) Determine the point of intersection of the two lines.

For i) i have set up parametric equations
(x)=(1-t)
(y)=(3-t)
and substituted in x=1 and y=2
t is not the same, therefore it does not lie on the line.
For part ii) I have no idea on how to start I tried substituting t as 1 and then 2 which was wrong.
I know that the dot product of two orthogonal vectors is 0

Thanks

2. May 27, 2013

### danago

In terms of the point (1,2) and any other general point (x,y) on the second line, can you find a vector (call it a) which is parallel to the line (i.e. it points in the same direction as the line)? Then, can you find a vector (call it b) that is parallel to the first line?

These two vectors, a and b, should be orthogonal. As you pointed out, their dot product should be zero. Can you come up with an equation based on this?