空間向量的加減法與係數積
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

x1

y1

z1

x2

y2

z2

向量的加減法與係數積

$ \overrightarrow{a} =($

,

,

)

$ \overrightarrow{b}=( $

,

,

$ ) $

1

a

b

2

\overrightarrow{a}-\overrightarrow{b}

 \overrightarrow{a}+\overrightarrow{b}

Reset

3

r

$ \overrightarrow{a} $

+

s

\overrightarrow{b}

x

y

z

s = 0 (slider from -5 to 5, step 1)
r = 0 (slider from -5 to 5, step 1)
z2 = 0 (slider from -5 to 5, step 0.1)
y2 = 0 (slider from -5 to 5, step 0.1)
x2 = 0 (slider from -5 to 5, step 0.1)
z1 = 0 (slider from -5 to 5, step 0.1)
y1 = 0 (slider from -5 to 5, step 0.1)
x1 = 0 (slider from -5 to 5, step 0.1)
O = (12.520846832723873, 0.8441957388024409)
β = 1.2217304763960306 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 3.9269908169872414 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
L = 5 (slider from 1 to 10, step 1)
a = Vector(O - L * v, O + L * v)
b = Vector(O - L * w, O + L * w)
z = Vector(O - L * u, O + L * u)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c = false
d = true
Q_2: 0.27 * Corner[2] + 0.73 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
多邊形1, e, q_2, q_3, f = Polygon(Corner[1], Q_2, Q_3, Corner[4])
g = Segment(Q_2, Q_3)
inputBox1 = Textfield(x1)
inputBox2 = Textfield(y1)
inputBox3 = Textfield(z1)
inputBox4 = Textfield(x2)
inputBox5 = Textfield(y2)
inputBox6 = Textfield(z2)
h = false
P1: O + x1 * u + y1 * v + z1 * w
P2: O + x2 * u + y2 * v + z2 * w
i = Vector(O, P1)
j = Vector(O, P2)
k = false
x3: y1 * z2 - y2 * z1
y3: z1 * x2 - z2 * x1
z3: x1 * y2 - x2 * y1
P3: O + x3 * u + y3 * v + z3 * w
q = Circle(O, 3)
p = Segment(O, P3)
A = Intersect(q, p)
p3: sqrt(x3^(2) + y3^(2) + z3^(2))
P4: O + 2 / p3 * P3
text12: "=(" + (x1 + x2) + "," + (y1 + y2) + "," + (z1 + z2) + ")"
text13: "=(" + (x1 - x2) + "," + (y1 - y2) + "," + (z1 - z2) + ")"
C2: O + (x1 - x2) * u + (y1 - y2) * v + (z1 - z2) * w
C1: O + (x1 + x2) * u + (y1 + y2) * v + (z1 + z2) * w
l = Vector(O, C1)
m = Vector(O, C2)
n = Vector(P2, P1)
o = false
inputBox7 = Textfield(r)
inputBox8 = Textfield(s)
C3: O + (r * x1 + s * x2) * u + (r * y1 + s * y2) * v + (r * z1 + s * z2) * w
t = Vector(O, C3)
text17: "=(" + (r * x1 + s * x2) + "," + (r * y1 + s * y2) + "," + (r * z1 + s * z2) + ")"