(Solved): Parts (a)-(d) are distinct from each other. (a) Consider the vectors u=i+2j+3k and v=3ij+2k. Fin ...

Parts (a)-(d) are distinct from each other. (a) Consider the vectors $u=i+2j+3k$ and $v=3i?j+2k$. Find the scalar projection (compv $u$ ) and vector projection (proj, $u$ ) of vector $u$ onto vector (b) Find the equation of the plane containing the points $A(1,4,?2),B(?2,3,1)$, and $C(3,2,?1)$. (c) Find the symmetric equations for the line through the points $\left(0,\frac{1}{2},1\right)$ and $(8,1,?6)$. (d) Let $F(x,y,z)=x^{2}y+x^{yz}$. Find the parametric equations of the normal line to the level surface $F(x,y,z)=0$ at the point $P(?1,1,0)$.