AIBU to ask for help with an A-Level Maths question?

[ALevelQuestion]

DD is doing a remote learning A-Level Maths course. She is stuck on a question (attached).

Does anyone have any ideas about how to tackle this?

Thanks for any advice.

My hands got sweaty just seeing that

i,j and k are all components of a vector in 3D.

So to add 2 vectors you need to add the separate components. Add up the i the add up the j then add up the k.

Question b is multiplying a vector by a scalar so all the components of r are multiplied by 3 Then added to s.

DH is a maths nerd and had a go.

He wasn’t too sure about d.

I think this is right

@Poorpigletsrevenge I agree with him that it’s 1/3.

I’m a maths teacher- although haven’t done vectors for a few years!

That's A-level?

I don’t even know why I clicked on this as I struggle to help the kids let alone answer an ALwvwl question 😂

@Snailsetssail He’s now feeling pretty pleased with himself, thanks

That was fun!

I even clicked on @Snailsetssails husbands answer, what’s wrong with me 😂

Oooh! I didn’t see D!

My solution to part d.

Isn’t part of the skill involved being able to look up their own help

Grrrr picture didn't post. Attempt 2

@Waiohwai

My solution to part d.

That’s for this - I couldn’t remember how to do that bit at all.

@EggysMom part a-c would be higher GCSE rather than A-Level.

I managed to do a, b & c but then gave up. My A level maths was 36 years ago and i'm a bit rusty.

Thank you so much all of you. I will show all the posts to DD!

Thanks for this - a very long time since I taught vectors.

Agree with PP
a) 2i + 2j + 4k
b) 8i + 8k
c) -4i + 4j

d) You only need to be concerned with the j component as it must be zero if as + r is parallel to vector i + k.

(3a -1)j = 0 so 3a - 1 = 0 => 3a = 1 => a = 1/3.

Do you have any more OP

What merry old goat said...

3 -1
-1 + 3
2 2

They may find it easier to convert to column vectors, as I've tried to show. Its a pain in the butt writing it this way in a Mumsnet message, so I only did the first little bit.

Aaaaand, it didn't format at all, sorry.

@rosegoldwatcher

Thanks for this - a very long time since I taught vectors.

Agree with PP
a) 2i + 2j + 4k
b) 8i + 8k
c) -4i + 4j

d) You only need to be concerned with the j component as it must be zero if as + r is parallel to vector i + k.

(3a -1)j = 0 so 3a - 1 = 0 => 3a = 1 => a = 1/3.

Do you have any more OP

Yes! More more!!

I’m feeling decidedly rusty!!

I know this is a bit off the point...but I've always wondered where you would actually use this kind of stuff? Do people actually use it in...I don't know, engineering...? Does it have a practical use or is it just learning for the sake of learning and passing exams? If it does have a practical use, then for what exactly?