Question 1011206
<pre>
Two non-zero vectors are perpendicular when
their dot product is zero.  

Let < x,y,z > be a vector perpendicular to <5,-7,-8>. 

Then,

<5,-7,-8> &#8729; < x,y,z > = 5x-7y-8z = 0

We can pick any values of x,y, and z that
will make the dot product above be 0.

For instance, since -8-7 =-15 and we can
make the 5 become a +15 to cancel that by 
multiplying it by 3, so one solution would 
be to choose y and z to be 1 each and x to
be 3.

So 

<5,-7,-8> &#8729; <3,1,1> = (5)(3)+(-7)(1)+(-8)(1)

= 15-7-8 = 0

So <3,1,1> is perpendicular to <5,-7,-8>

There are many other possibilities.

Edwin</pre>