# Parallelism of Time-varying Vectors

baldbrain

## Homework Statement

This is a solved problem, but I haven't understood a few things.
I've marked out sections of the solution in white for convenience. The markings are positioned where that particular section ends. In part (1), how did they just assume
f1(0) = 2, f2(0) = 3, g1(0) = 3, g2(0) = 2
f1(1) = 6, f2(1) = 2, g1(1) = 2, g2(1) = 6

And, in part (4), what is this 'intermediate value theorem' that they've used?
We've just done the basics on vectors, so I have no idea where this 'intermediate value theorem' came from....
Then, in part (2) they say we have to prove that
f1(t).g2(t) - f2(t).g1(t) = 0
And in part (4), they just implied the same thing from out of nowhere & voila! The problem's over!

#### Attachments

Gold Member
Your objections are valid. These values seem to come out of nowhere.

The intermediate value theorem simply says that if a continuous function has two values, then it must also have every value in between the two.

• baldbrain
baldbrain
The intermediate value theorem simply says that if a continuous function has two values, then it must also have every value in between the two.
That's so obvious (assuming the function is defined on R). We've done this as a deduction of continuity, not as a separate theorem.

baldbrain
These values have a pattern...
2 3 3 2
6 2 2 6

Ok professor 