Finding scalars from vectors
(Note: the bold letters are vectors.)
"Find the scalars, α and β and such that
(i) 3i + j is parallel to αi - 4j
(ii) 3i + β(j - k) is parallel to i - 4j+ 4k
(iii) 3i + γ(j + 3k) has the same length as 12i - 5k"
I first assumed that since the vectors are parallel, they would be equal to each other. So, as for (i), and assuming that v = 3i + j, I found |v| as assumed that would be the length and thought that finding the length of the other vector through solving it that way would be the right approach. However, I realised that it isn't.
I did have a peep at the answers although, that's all that was there so that was hardly any help. (If it is needed - (i)-12 (ii)-12 (iii) ±4). I tried looking over my course notes and even the appropriate section from my textbook but, I can't find anything that is similar to this question.