p1_mrg_vector1 -- Sage

#initialize vectors in R^3 a=vector([1,2,3]) a

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(1,\,2,\,3\right)$

b=vector([-1,0,5]) b

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(-1,\,0,\,5\right)$

#vector sums c=a+b show(c) d=a-b show(d)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0,\,2,\,8\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(2,\,2,\,-2\right)$

#vector plots a.plot(rgbcolor='red')+b.plot(rgbcolor='blue')+c.plot(rgbcolor='green')

#vector magnitudes lenA=norm(a) lenB=norm(b) lenC=norm(c) lenD=norm(d) show(lenA) show(lenB) show(lenC) show(lenD)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{14}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{26}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sqrt{17}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sqrt{3}$

#scalar product e=a*b e

 $\newcommand{\Bold}[1]{\mathbf{#1}}14$

f=sum(ai*bi for ai,bi in zip(a,b)) f

 $\newcommand{\Bold}[1]{\mathbf{#1}}14$

g=a.dot_product(b) g

 $\newcommand{\Bold}[1]{\mathbf{#1}}14$

#find theta between vector a and b using dot product theta1=arccos(e/(lenA*lenB)) show(n(theta1)) theta2=theta1*180/pi show(n(theta2))

 $\newcommand{\Bold}[1]{\mathbf{#1}}0.746898593069036$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}42.7941371071149$

p1_mrg_vector1

3071 days ago by LAC2011