I have two exercises here that are giving me problems. I don't have a strong enough conceptual grasp on the material I guess.
Find the value k so that the points A=(2,-1), B=(1,4), and C=(k,9) are aligned.
Find the values of a and b so that the two lines r: ax-y+2=0 and s: bx+6y-9=0 are perpendicular and also so that the second line passes through the point P=(1,1).
Additionally, if anyone has a recommendation for sources to brush up on these kinds of exercises, I feel they would greatly strengthen my comprehension for the linear algebra class I'm taking.
That said, if there are multiple paths to solutions to these exercises, ideally I would like to relate them to concepts such as vectors, dot product, etc. Thank you again.