Hi everyone, the question above is for my linear algebra assignment and it had me thinking a lot. I am not sure how to proceed. My attempt was to find the norm of u, which is 1/2, and the norm of v, which is 2. (correct me if I'm wrong).
However, I don't how to proceed when the vector is in the norm notation.
I thank everyone in advance.
Note that $$\vec a \times (\vec b \times \vec c) = \vec b(\vec a\cdot\vec c)-\vec c (\vec a \cdot \vec b).$$ Therefore, $$\vec u \times (\vec u \times \vec v) = \vec u(\vec u\cdot\vec v)-\vec v (\vec u \cdot \vec u) = -\frac{1}{4}\vec v \implies \|\vec u \times (\vec u \times \vec v)\| = \frac{1}{4}\|\vec v\|=?$$