Vector Scaling Demonstration

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2016-07-15 11:00

Vector Geometric Construction

This example dynamically illustrates the meaning of multiplying a vector by a scalar quantity, covering core concepts like vectors, scalar multiplication, and vector length transformation. It uses commands such as Vector, Line, Length, Circle, Intersect, Dilate, Mirror, and Translate in GeoGebra for construction. Ideal for high school students learning vector operations and geometric interpretations.

GeoGebra Commands & Parameters

Vector(A, B) → u
Line(C, u) → f
Length(u) → b
Circle(C, b) → c
Intersect(c, f, 2) → D
Circle(D, b) → d
Intersect(d, f, 2) → E
Circle(E, b) → e
Intersect(e, f, 2) → F
Circle(F, b) → g
Intersect(g, f, 2) → G
Circle(G, b) → h
Intersect(h, f, 2) → H
Circle(H, b) → k_2
Intersect(k_2, f, 2) → I
Circle(I, b) → p
Intersect(p, f, 2) → J
Circle(J, b) → q
Intersect(q, f, 2) → K
Circle(K, b) → r
Intersect(c, f, 1) → L
Circle(L, b) → s
Intersect(s, f, 1) → M
Circle(M, b) → t
Intersect(t, f, 1) → N
Circle(N, b) → c_1
Intersect(c_1, f, 1) → O
Circle(O, b) → d_1
Intersect(d_1, f) → P, Q
Circle(P, b) → e_1
Intersect(e_1, f, 1) → R
Circle(R, b) → f_1
Intersect(f_1, f, 1) → S
Circle(S, b) → g_1
Intersect(g_1, f, 1) → T
Circle(T, b) → h_1
Intersect(h_1, f, 1) → U
Dilate(C, If[0 < i ≤ 1, 1 - i, 0], D) → C'
Dilate(D, If[0 < i ≤ 1, 1 - i, 0], E) → D'
Dilate(E, If[0 < i ≤ 1, 1 - i, 0], F) → E'
Dilate(F, If[0 < i ≤ 1, 1 - i, 0], G) → F'
Dilate(G, If[0 < i ≤ 1, 1 - i, 0], H) → G'
Dilate(H, If[0 < i ≤ 1, 1 - i, 0], I) → H'
Dilate(I, If[0 < i ≤ 1, 1 - i, 0], J) → I'
Dilate(J, If[0 < i ≤ 1, 1 - i, 0], K) → J'
Mirror(C', C) → C''
Mirror(D', C) → D''
Mirror(E', C) → E''
Mirror(F', C) → F''
Mirror(G', C) → G''
Mirror(H', C) → H''
Mirror(I', C) → I''
Mirror(J', C) → J''
Vector(C, C') → v
Vector(D, D') → w
Vector(E, E') → j
Vector(F, F') → l
Vector(G, G') → m
Vector(H, H') → n
Vector(I, I') → u_1
Vector(J, J') → v_1
Vector(C, C'') → w_1
Vector(L, D'') → a_1
Vector(M, E'') → b_1
Vector(Q, F'') → i_1
Vector(O, G'') → j_1
Vector(P, H'') → k_1
Vector(R, I'') → l_1
Vector(S, J'') → m_1
Vector(C, V) → n_1
Translate(E, n_1) → E'_1
Translate(F, n_1) → F'_1
Translate(G, n_1) → G'_1
Translate(H, n_1) → H'_1
Translate(I, n_1) → I'_1
Translate(J, n_1) → J'_1
Translate(K, n_1) → K'
Translate(L, n_1) → L'
Translate(M, n_1) → M'
Translate(Q, n_1) → Q'
Translate(O, n_1) → O'
Translate(P, n_1) → P'
Translate(R, n_1) → R'
Translate(S, n_1) → S'
Translate(T, n_1) → T'
Translate(D, n_1) → D'_1
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], D'_1) → V'
Vector(V, V') → p_1
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], E'_1) → V'_1
Vector(V, V'_1) → q_1
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], F'_1) → V'_2
Vector(V, V'_2) → r_1
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], G'_1) → V'_3
Vector(V, V'_3) → s_1
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], H'_1) → V'_4
Vector(V, V'_4) → t_1
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], I'_1) → V'_5
Vector(V, V'_5) → u_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], J'_1) → V'_6
Vector(V, V'_6) → v_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], K') → V'_7
Vector(V, V'_7) → w_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], L') → V'_8
Vector(V, V'_8) → a_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], M') → V'_9
Vector(V, V'_9) → b_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], Q') → V'_{10}
Vector(V, V'_{10}) → c_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], O') → V'_{11}
Vector(V, V'_{11}) → d_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], P') → V'_{12}
Vector(V, V'_{12}) → e_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], R') → V'_{13}
Vector(V, V'_{13}) → f_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], S') → V'_{14}
Vector(V, V'_{14}) → g_2
Dilate(V, If[1 < i ≤ 2, 2 - i, 0], T') → V'_{15}
Vector(V, V'_{15}) → h_2