Vectors Question A Level Maths!!!

https://www.quora.com/profile/Bravewarrior/p-149641818
Here is the question. I cannot find the solution anywhere and only scored 3/9 marks on this question (its from a test I did). I'm also really sorry that it's quite messy, I was confused so was trying different ways of solving it. Can someone please help me out with this question? Thank you!

https://www.quora.com/profile/Bravewarrior/p-149641818
Here is the question. I cannot find the solution anywhere and only scored 3/9 marks on this question (its from a test I did). I'm also really sorry that it's quite messy, I was confused so was trying different ways of solving it. Can someone please help me out with this question? Thank you!

Just express the lines KM and ML in the usual line form so
p(a,b,c) + mu*d(a,b,c)
where p is the position vector of a point on the line and d is the direction vector, then equate and solve for the scalars mu and ...

It would make sense for KM if p = K and d = KM say, then the intersection point should correspond to mu=1/2. Similar for the other line.

For this question, you could almost just write down the intersection point P(a,b,c) and verify it lies on both lines. Guessing P must be the centre of the cuboid so (a+b+c)/2. But the previous way is a better way to go.

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