1.Find $\displaystyle \vec{a} x \vec{b}$(Vectorial product) if $\displaystyle \vec{a}=3\vec{m}+2\vec{n}$, $\displaystyle \vec{b}=\vec{m}+5\vec{n}$ and $\displaystyle |\vec{m}|=|\vec{n}|=1$. (Angle between m and n is 90 degrees.)

2.We have vectors $\displaystyle \vec{a}=(0,2\lambda,\lambda), $ $\displaystyle \vec{b}=(2,2,1)$ and $\displaystyle \vec{c}=(-1,-2,-1)$

a) Find $\displaystyle \vec{d}$ from this conditions: $\displaystyle \vec{a}x\vec{b} = \vec{c}x\vec{d}$ and $\displaystyle \vec{a}x\vec{c} = \vec{b}x\vec{d}$ (Vectorial product).

b) Prove that vectors $\displaystyle \vec{a} - \vec{d}$ and vectors $\displaystyle \vec{b} - \vec{c}$ are colinear.

c) Find $\displaystyle \lambda$ from condition $\displaystyle (\vec{a}-\vec{b})*\vec{c}=\vec{a}*\vec{c}+\lambda$

3. Write equation of normal from point $\displaystyle M(2,3,1)$ into line:$\displaystyle l: \frac{x+1}{2}=\frac{y-0}{-1}=\frac{z-2}{3}$.

Thank you.