Triangles and trigonometry help please

[kitchenisland]

Before I show myself as a 1D 10T to my teenage son can anyone advise how I solve this math problem.

It's only GvSE day tomorrow and he now says he doesn't understand this but it's a long time since I did this
sort of thing and don't want to advise him incorrectly.

Any help gratefully received.

And I do realise it is GCSE.

Although back in my day they weren't. That's how long ago it was.

That's not trig, it's to do with vectors. See if this video helps.

https://corbettmaths.com/2021/07/05/vectors-videos/

Thank you. He is now watching the video. Why he hasn't already done this is beyond me. I know he has access to corbettmaths.
Aah yes sorry we have just worked out the trig question. Might not be correct though

It's hard to explain without a picture (of my working out). Please imagine a little arrow above letters like OD.

Work out OD, which is OB + BD 3b+2a +b. Collecting like terms gives 2a+4b

Work out AC. It's 2/3rds of the way down AB. AB is -3a +bc, so AC is 2/3 (-3a+3b) or -2a+2b

Work out OC (OA+AC) 3a + (-2a) +2b collected together it is a+2b

Since OC = a+2b and OD = 2a +4b (i.e. twice OC), they are on the same line, they have the same vector but a different magnitude (size).

They also have a common point C which makes them on the same line rather than parallel.

This might be a better video, as it's a very similar question.

https://www.mathsgenie.co.uk/vectors.html

Second video- Harder vectors 1, start the video at about 7:08

Thank you for this.
Yup as I suspected it is way above my pay grade!