906 MrG What is R^3? -- Sage

#9 p623 from (0,0,0) to (4,1,2) v=vector([4,1,2]) show(v) plot(v)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(4,\,1,\,2\right)$

#23 p623 from (3,2,-1) to (5,6,0) w=vector([2,4,1]) show(w) plot(w)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(2,\,4,\,1\right)$

#27 p623 magnitude of <3,-6,-2> u=vector([3,-6,-2]) show(abs(u)) plot(u)

 $\newcommand{\Bold}[1]{\mathbf{#1}}7$

#33 p623 find 2*v+3*w if v=<3,-5,2> and w=<-2,3,2> v=vector([3,-5,2]) w=vector([-2,3,2]) show(2*v) show(3*w) show(2*v+3*w) p1=plot(2*v,color='red') p2=plot(3*w,color='green') sum=plot(2*v+3*w) show(p1+p2+sum,aspect_ratio=1)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(6,\,-10,\,4\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(-6,\,9,\,6\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0,\,-1,\,10\right)$

#45 p623 v.dot_product(w)=abs(v)*abs(w)*cos(t) #45 p623 find t if v=<1,-1,0> and w=<1,1,1> v=vector([1,-1,0]) w=vector([1,1,1]) d=v.dot_product(w) show(d) show(abs(v)) show(abs(w)) show(d/abs(v)/abs(w)) show(arccos(d/abs(v)/abs(w))) show(arccos(d/abs(v)/abs(w))*180/pi) v1=plot(v,color='red') w1=plot(w,color='green') show(v1+w1,aspect_ratio=1)

 $\newcommand{\Bold}[1]{\mathbf{#1}}0$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{3}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}0$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, \pi$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}90$

906 MrG What is R^3?

2751 days ago by MATH4R2013