Let vec$(v)=5$vec$(i)6$vec$(j)3$vec$(k)$ and vec$(w)=4$vec$(i)-6$vec$(j)-7$vec$(k).$ Find the following:

a$)9$vec$(v)-4$vec$(w)$

b$)$ vec$(v)*vec(w)$

c$)$ vec$(w)$vec$(v)$

d$)pro{j}_{\frac{?}{\text{b}\text{a}\text{r}}(v)}$vec$(W)$

e$)$ the angle between vec$(v)$ and vec$(w)$

f$)$ vec$(u{)}_{\frac{?}{\text{b}\text{a}\text{r}}(w)}$

Find the area of the triangle whose vertices are $(2,3,4),(0,3,5),$ and $(0,0,6).$

Three forces are acting on an object. The first force is $40$ N acting at an angle of $60$ above the horizontal and to the left. The second force is $50$ N acting at an angle of $40$ above the horizontal to the right. The third force is $60$ N acting straight down. What additional force is required to keep the object stationary?

Find the tangent line to vec$(r)(t)=(3t^2-4)vec(i)(6t^{3}2t)vec(j)$ when $t=3.$

Give parametric equations for the line from $(9,3,7)$ to $(2,6,8).$

Given the vectors vec$(v)$ and vec$(w)$ below, sketch the following:

a$)$ vec$(v)$ vec$(w)$

b$)$ vec$(v)-$vec$(w)$

c$)-\frac{2}{b}ar(v)$