三维向量探索
几何画板及绘图内容加载中,请稍等……
这个范例演示了三维空间中的向量。核心数学概念包括向量的加减法、点乘和叉乘。通过使用GeoGebra命令如Vector、Translate、Line等,可以直观地展示向量的几何意义和运算规则。适合高中及以上学生学习三维向量的相关知识。
GeoGebra 命令及参数
Vector(A) → uVector(B) → vVector(C) → wTextfield(k) → InputBox1Textfield(l) → InputBox2Textfield(m) → InputBox3Translate(D, c) → D'Vector(D, D') → fTranslate(E, b) → E'Vector(E, E') → gTranslate(E', d) → E''Vector(E', E'') → hTranslate(F, e) → F'Vector(F, F') → iTextfield(x1) → InputBox4Textfield(y1) → InputBox5Textfield(z1) → InputBox6Textfield(x2) → InputBox7Textfield(y2) → InputBox8Textfield(z2) → InputBox9Textfield(x3) → InputBox10Textfield(y3) → InputBox11Line(G, v) → rOrthogonalLine(A, r, space) → sIntersect(s, r) → IVector(I) → pSegment(A, I) → f_1OrthogonalLine(A, o) → g_1OrthogonalLine(B, o) → h_1OrthogonalLine(C, o) → i_1OrthogonalLine(C, zAxis, space) → j_1OrthogonalLine(B, zAxis, space) → k_1OrthogonalLine(A, zAxis, space) → l_1Intersect(g_1, o) → JIntersect(h_1, o) → KIntersect(i_1, o) → LSegment(A, J) → m_1Segment(B, K) → n_1Segment(C, L) → p_1Intersect(k_1, zAxis) → MIntersect(l_1, zAxis) → NIntersect(j_1, zAxis) → OSegment(A, N) → q_1Segment(B, M) → r_1Segment(C, O) → s_1OrthogonalLine(J, xAxis, space) → t_1OrthogonalLine(J, yAxis, space) → a_1OrthogonalLine(K, yAxis, space) → b_1OrthogonalLine(K, xAxis, space) → c_1OrthogonalLine(L, yAxis, space) → d_1OrthogonalLine(L, xAxis, space) → e_1Intersect(yAxis, d_1) → PIntersect(a_1, yAxis) → QIntersect(b_1, yAxis) → RIntersect(xAxis, t_1) → SIntersect(c_1, xAxis) → TIntersect(e_1, xAxis) → USegment(L, U) → f_2Segment(L, P) → g_2Segment(K, R) → h_2Segment(K, T) → i_2Segment(J, S) → j_2Segment(J, Q) → k_2OrthogonalLine(D, o) → l_2OrthogonalLine(E, o) → m_2OrthogonalLine(F, o) → n_2OrthogonalLine(D, zAxis, space) → p_2OrthogonalLine(E, zAxis, space) → q_2OrthogonalLine(F, zAxis, space) → r_2Intersect(p_2, zAxis) → VIntersect(q_2, zAxis) → WIntersect(r_2, zAxis) → ZIntersect(l_2, o) → A_1Intersect(m_2, o) → B_1Intersect(n_2, o) → C_1OrthogonalLine(A_1, xAxis, space) → s_2OrthogonalLine(B_1, xAxis, space) → t_2OrthogonalLine(C_1, xAxis, space) → a_2OrthogonalLine(A_1, yAxis, space) → b_2OrthogonalLine(B_1, yAxis, space) → c_2OrthogonalLine(C_1, yAxis, space) → d_2Intersect(s_2, xAxis) → D_1Intersect(t_2, xAxis) → E_1Intersect(a_2, xAxis) → F_1Intersect(b_2, yAxis) → G_1Intersect(c_2, yAxis) → H_1Intersect(d_2, yAxis) → I_1Segment(D, V) → e_2Segment(D, A_1) → f_3Segment(A_1, D_1) → g_3Segment(A_1, G_1) → h_3Segment(E, W) → i_3Segment(E, B_1) → j_3Segment(B_1, H_1) → k_3Segment(B_1, E_1) → l_3Segment(F, Z) → m_3Segment(F, C_1) → n_3Segment(C_1, I_1) → p_3Segment(C_1, F_1) → q_3Textfield(z3) → InputBox12
AI 绘图提示语参考
绘制三维空间中的向量及其运算。首先创建三个向量u、v、w,然后通过平移和向量运算生成新的向量f、g、h、i。接着输入x1、y1、z1等坐标值,构造点和线,利用点和线的交点生成新的向量和线段,最终展示向量的加减法、点积和叉积。
以上提示语为根据原始绘图命令整理而来,仅供参考。