Question

[Calculus:Vectors]

Hello, in the following pdf, Part II : problem 3 : b. I tried to solve it but my solution is wrong, the problem is I don't why it's wrong.

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_pset1sol.pdf

My wrong solution

https://www.dropbox.com/s/zyrvrsgo6xs2oe2/Pset%2C%20last%20proplem.png?dl=0

Answer 1

The correct solution

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/problem-set-1/MIT18_02SC_pset1sol.pdf

Answer 2

you have posted the solutions twice, ie no original problem here....

Answer 3

The original problem is that I don't know why my solution is wrong.

Answer 4

I want to know where I did go wrong to avoid it in the future, with god's will.

Answer 5

if you expand out your answer, you get their answer.

it is far easier to use the definition \(\vec a \bullet \vec b = |a| |b| \cos \theta\) for magnitude; and then to assign the direction of the vector , as they have broadly done

than it is to do a full dot product of \(<\cos \alpha, \sin \alpha> * <\cos (\alpha + \beta), \sin (\alpha + \beta)>\)

Answer 6

You're correct, thanks a lot for your help.