How to Determine Perpendicular and Collinear Vectors with 2 Variables

[STUDENT vs HOMEWORK]

Homework Statement

This problem actually has 2 parts.
For vectors a= (2,p,8) and b= (q,4,12), determine the values of p and q so that the vectors are a)perpendicular b) collinear

textbook answer: a) p= 1 and q= -50 (answers may vary) b) p= 8/3 and q=3

Homework Equations

a*b = 0

a*b = a₁b₁ + a₂b₂ + a₃b₃

3. The Attempt at a Solution
So for the first part, I used a*b = 0 and I don't know how to do the second part

a*b = 0
(2,p,8)*(q,4,12) = 0
2q + 4p + 96 =0

I tried isolating p and q and substituting them but I end up with 0.

 

[Orodruin]

First part: What do you mean by "end up with zero"? You are supposed to pick p and q so that the inner product is zero.

Second part: What does it mean for two vectors to be collinear?