I have a question in my work where I have to find the values of a and b such that (a,2,3)^T and (1,2,b-2)^T are not perpendicular. (I have chosen random values as an example, as I'm not asking anyone to do my work for me)
The way I was going to work it out if they didn't need to be transposed was to find the values a and b to be perpendicular and then state that they cannot equal those values.
Doing this using the dot product of any two vectors (a1,a2,a3) and (b1,b2,b3) =a1b1+a2b2+a3b3. Then simplifying the expression to solve for a and b.
Where I need help however (assuming that the above is appropriate) is transposing a vector and then finding the two vectors to NOT be perpendicular.