finkeljo said:
Well I know the scalar product(dot product) is defined to be:
u*v=||u||*||v||cos\theta
I've been lookin at it for the past hour or so and can't put it together how this definition applies.
Ok, so here's the main formula that we'll use to solve the problem.
u, and v can be any vector. So, if u = v = a, that means the angle \theta between those 2 vectors is 0, right? Both u, and v are the same vector, so there's no angle separating them.
Using the formula above, we have:
\mathbf{a} * \mathbf{a} = ||\mathbf{a}|| ||\mathbf{a}|| \cos (0)
\Rightarrow \mathbf{a} * \mathbf{a} = ||\mathbf{a}|| ^ 2 (since cos(0) = 1)
\Rightarrow ||\mathbf{a}|| = \sqrt{\mathbf{a} * \mathbf{a}}, which boils down to the formula Hoot showed you:
Hootenanny said:
Well you also know that for any vector, a,
||a|| = (a.a)1/2
Does that help?
Now, since
u, and
v are both vectors,
u +
v is also a vector. How can we determine ||u + v||. How can we
apply the
above formula?
Let's assume that you can get over this step. After applying the formula, you will arrive at some expression. The next step is to
expand it. Then use the first formula
\mathbf{u} * \mathbf{v} = ||\mathbf{u}|| ||\mathbf{v}|| \cos (\theta)
to simplify that expression, and arrive at the desired result. Also note that w, and v in your problem are unit vectors, i.e: ||
u|| = ||
v|| = 1
This one is very basic, sorry I cannot be more detailed, or otherwise, I'll be solving it for you. Hopefully you can go from here, right? :)
