What topic is this question?

I can't really start reading up on this question as I don't know what topic it is. Can anyone help?

True or false: if u is perpendicular to v and w thenuis perpendicular tov+ 2w.Give a proof if true, or a counterexample if false

I can't really start reading up on this question as I don't know what topic it is. Can anyone help?

True or false: if u is perpendicular to v and w thenuis perpendicular tov+ 2w.Give a proof if true, or a counterexample if false

Consider $\mathbf{u} \cdot (\mathbf{v} + 2\mathbf{w})$

I mean I'm thinking vectors but that's a pretty big domain. And I'm not really sure what multiplying them would do? I don't really understand why u being perpendicular would mean you multipy. Nor can I visualise it being perpendicular to two things either, I really just need to know some background.

Yes, or rather, what does this mean practically?

Yes, or rather, what does this mean practically?

I'd look for a counter-example. The dot product being zero has a caveat.

I mean I'm thinking vectors but that's a pretty big domain. And I'm not really sure what multiplying them would do? I don't really understand why u being perpendicular would mean you multipy. Nor can I visualise it being perpendicular to two things either, I really just need to know some background.

Surely if you're being asked this question as part of a uni course then you've been given a context for it, i.e. you know what module you're studying and what objects you're working with?

You know, I'm getting very concerned about the way Universities seem to be teaching mathematics these days. Apparently it's now the norm to set questions in areas that aren't covered in the course - indeed, speaking to the students it seems likely no mathematics at all has actually been covered since term started. What's more, there seem to be severe bandwidth limits on uploads, preventing the poor students from ever being able to upload anything even remotely resembling an attempt at answering a question.

I'd look for a counter-example. The dot product being zero has a caveat.

Surely if you're being asked this question as part of a uni course then you've been given a context for it, i.e. you know what module you're studying and what objects you're working with? I mean are you doing a Geometry course where vectors can be used to represent real physical entities like lines or sides of a shape and you can see what "perpendicular" means, or are you doing a more abstract linear algebra course where you're given a purely abstract definition of perpendicularity for two objects??

I mean yes but I have probably with online teaching and everything missed where perpendicularness comes into things, I see you misunderstand me so let me show you what I mean.

I am 90% sure this is the wrong direction.

counter e.g. >> v = i + j , w = 2i + 2j


v * w = i * 2i + j * 2j = 2i + 2j ??? (not sure if this is correct at all)


v + 2w = (i + j) + (2i + 2j) = 3i + 3j != v*w


I don't see where perpendicularness comes into it?

I mean yes but I have probably with online teaching and everything missed where perpendicularness comes into things, I see you misunderstand me so let me show you what I mean.

Well, as we suggested above, you absolutely need a definition of what "perpendicular" means for your vectors. And also you are supposed to be working with 3 vectors u, v and w, not just v and w, so what you've written above isn't a "proof" (or counterexample) for your original statement.

Which subject are you studying and where? Did you do A-level Maths?