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# vectors watch

1. can anyone give me a hard vector question?
2. (Original post by berivan123)
can anyone give me a hard vector question?
It wouldn't be on a GCSE paper but something like this can be challenging for most GCSE students:

Use vectors to prove that joining the midpoints of the sides of any quadrilateral will form a parallelogram.
3. a)
The lines and have vector equations

and

respectively.

Show that the line and do not intersect.

b)

Find the shortest distance between the lines and .

(You may not use the vector product or any standard formula that calculates the distance between lines in this question).
4. (Original post by B_9710)
...
Could be a bit too advanced for GCSE level
5. 1. Show that the angle between any two faces of a regular octahedron is .

2. Find the ratio of the volume of a rectangular octahedron to the volume of the cube whose vertices are the centres of the faces of the octahedron.
6. (Original post by notnek)
Could be a bit too advanced for GCSE level
I know, I didn't realise it was a GCSE thread until after I'd posted.

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