yeah I get what you mean, these sort of questions are annoying when you kinda logically already know why it’s not true. Unfortunately you kinda have to use an actual proof unless the question says “explain”, for example the hsc marking criteria for this q requires it. You just kinda have to figure out how to logically write out your thoughts, e.g parallel -> scalar multiples.@carrotsss so for the hsc one for part a would u have to do the contradiction thing or could u just explain that if they different components, and not parallel then each component is equal to zero so u and v is = 0. Cuz like for questions thats what we just do right without thinking but this is asking us to show it so its wierd cuz its so obvious- so it makes sense to use contradiction for these stuff and i was also taught that- but like could u just explain that instead.
I did this question in class a couple weeks ago, and the way I approached it was to rearrange the equations so that u was a scalar multiple of v, which means if lambda/mu are non-zero, then they are parallel. Then I just did a simple contradiction statement because they aren’t parallel, so hence they must be zero - the hsc solution does a similar thing, it’s worth giving it a look.