Using vectors prove that

a)

b)

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- February 3rd 2010, 06:46 AMns1954ST and CT by vectors
Using vectors prove that

a)

b) - February 3rd 2010, 08:03 AMGrandad
Hello ns1954First, note that the dot product of vectors and is:

, where is the angle between the vectors

Next, we'll prove the second result first, because it's more straightforward.

Consider the points on the unit circle . The radii make angles with the positive -axis, measured anticlockwise. So , measured anticlockwise from to .

Using vector notation, we have:

, since .

Then the proof of the first result. Note that:, using the result just provedThen, with the point defined as above, consider the point - see the attached diagram. Then the radius makes an angle with the -axis. Therefore .

Then, as before:

- February 3rd 2010, 09:46 AMns1954
Is it possible to prove this without using koordinate vectors? To say so, more evidence direct profe, like for cosine theorem.