14  OJS figures

fsab = Object {ax: 1, ay: 0.5, bx: 0.5, by: 1}
ab = Array(1) [Object]
−2.0−1.5−1.0−0.50.00.51.01.52.0−2.0−1.5−1.0−0.50.00.51.01.52.0aba + b
Figure 14.1: Adding vectors a and b. 
viewof fsab = 
Inputs.form({
  ax: Inputs.range([-1,1], {
    format: (x) => x,
    value: 1, 
    step: .01, 
    label:html`<em>a<sub>x</sub></em>`,
    labelStyle: "width: 50px"
  }),
  ay: Inputs.range(
    [-1,1], 
    {value: 0.5, 
     step: .01, 
     label: html`<em>a<sub>y</sub></em>`}),
  bx: Inputs.range(
    [-1,1], 
    {value:0.5, 
     step: .01, 
     label: html`<em>b<sub>x</sub></em>`}),
  by: Inputs.range(
    [-1,1], 
    {value: 1, 
     step: .01, 
     label: html`<em>b<sub>y</sub></em>`})
  })
ab=[{x0: 0, 
     y0: 0, 
     ax: fsab.ax, 
     ay: fsab.ay, 
     bx: fsab.bx, 
     by: fsab.by, 
     abx: fsab.ax + fsab.bx, 
     aby: fsab.ay + fsab.by, 
     theta: Math.atan2(fsab.ay + fsab.by, fsab.ax + fsab.bx), 
     thetaa: Math.atan2(fsab.ay, fsab.ax), 
     thetab: Math.atan2(fsab.by, fsab.bx), 
     a: 'a', 
     b: 'b', 
     ab:'a + b', 
     fill: '#ffffff', 
     r: 200}]


Plot.plot({height: 600, width: 600,
x: {domain: [-2, 2], grid: true, ticks: 9},
y: {domain: [-2, 2], grid: true, ticks: 9},
style: {
    fontSize: 14, fontFamily: "equity_text_a_tab"
  },
marks: [
  Plot.ruleY([0]),
  Plot.ruleX([0]),
  Plot.arrow(
    ab, 
    {x1: "x0", 
     y1: "y0", 
     x2: "ax", 
     y2: "ay", 
     stroke: "#8B1A1A", 
     headAngle: 30, 
     headLength: 10, 
     fill: "#8B1A1A"}),
  Plot.arrow(
    ab, 
    {x1: "ax", 
     y1: "ay", 
     x2: "abx", 
     y2: "aby", 
     stroke: "#27408B", 
     headAngle: 30, 
     headLength: 10, 
     fill: "#27408B", 
     alpha: .5}),
  Plot.arrow(
    ab, 
    {x1: "x0", 
     y1: "y0", 
     x2: "abx", 
     y2: "aby", 
     stroke: "#51315E", 
     headAngle: 30, 
     headLength: 10, 
     fill: "#51315E"}),
  Plot.dot(
    ab, 
    {x: (d) => d.ax/2, 
     y: (d) => d.ay/2, 
     fill: "fill", 
     r: 7}),
  Plot.dot(
    ab, 
    {x: (d) => d.ax + d.bx/2, 
     y: (d) => d.ay + d.by/2, 
     fill: "fill", 
     r: 7}),
  Plot.dot(
    ab, 
    {x: (d) => d.abx/2, 
     y: (d) => d.aby/2, 
     fill: "fill", 
     r: 18}),
  Plot.text(
    ab, 
    {x: (d) => d.ax/2, 
     y: (d) => d.ay / 2, 
     text: 'a', 
     rotate: (d) => Math.atan(Math.tan(d.thetaa)) * -180 / Math.PI, 
     fill: '#8B1A1A'}),
   Plot.text(
     ab, 
     {x: (d) => d.ax + d.bx/2, 
      y: (d) => d.ay + d.by / 2, 
      text: 'b', 
      rotate: (d) => Math.atan(Math.tan(d.thetab)) * -180 / Math.PI, 
      fill: '#27408B'}),
  Plot.text(
    ab, 
    {x: (d) => d.abx/2, 
     y: (d) => d.aby / 2, 
     text: 'ab', 
     rotate: (d) => Math.atan(Math.tan(d.theta)) * -180 / Math.PI, 
     fill: '#51315E'})
]})
fs = Object {xi: 1, yi: 1, a: 2}
ax = 2
ay = 2
theta = 0.7853981633974483
dd = Array(1) [Object]
ns = "oi-3a86ea"
−5−4−3−2−1012345−5−4−3−2−1012345(2.00, 2.00)
Figure 14.2: Multiplying a vector by a scalar changes its magnitude. 
viewof fs = 
Inputs.form({
  xi: Inputs.range([-1,1], {
    format: (x) => x,
    value: 1, 
    step: .01, 
    label: md`*x* `,
    labelStyle: "width: 50px"
  }),
  yi: Inputs.range(
    [-1,1], 
    {value: 1, 
     step: .01, 
     vertical: true, 
     label: md`*y*`}),
  a: Inputs.range(
    [-5,5], 
    {value: 2, 
     step: .01, 
     label: md`*a* `, 
     description: 'Scalar'})
  })
ax = fs.xi * fs.a
ay = fs.yi * fs.a
theta=Math.atan2(ay,ax)
dd=[{
  x: fs.xi, 
  y: fs.yi, 
  ax: ax, 
  ay: ay, 
  x0: 0, 
  y0: 0, 
  a: fs.a, 
  theta: theta }]

ns = Inputs.range().classList[0]

html`
<style>
form.${ns} {--input-width: 600px; --label-width: 15px;}
.${ns}-input>input[type=number] {flex-shrink:6;}
</style>
`
Plot.plot({height: 600, width: 600,
x: {domain: [-5, 5], grid: true, ticks: 9},
y: {domain: [-5, 5], grid: true, ticks: 9},
style: {
    fontSize: 14, 
    fontFamily: "equity_text_a_tab"
  },
marks: [
Plot.ruleY([0]),
Plot.ruleX([0]),
Plot.arrow(
  dd, 
  {x1: "x0", 
   y1: "y0", 
   x2: "ax", 
   y2: "ay", 
   stroke: "#8B1A1A", 
   headAngle: 30, 
   headLength: 10, 
   fill: "#8B1A1A"}),
Plot.arrow(
  dd, 
  {x1: "x0", 
   y1: "y0", 
   x2: "x", 
   y2: "y", 
   stroke: "#27408B", 
   headAngle: 30, 
   headLength: 10, 
   fill: "#27408B"}),
  Plot.text(
    dd, 
    {x: (d) => d.ax + .3 * Math.cos(d.theta), 
     y: (d) => d.ay + .3 * Math.sin(d.theta), 
     text: (d) => '('+(d.ax).toFixed(2)+', '+(d.ay).toFixed(2)+')'})
]})