台灣黑皮歐巴桑的學習祕笈

中英文版(高二上數學)第三章第二節 平面向量的內積(向量內積的定義、平面向量的正射影與高、平面向量與柯西不等式)

*高中數學 淺談外積內積定義
https://www.youtube.com/watch?v=NfsaHnPBuJY

*向量的內積是什麼？看完馬上就懂！【平面向量】
https://www.youtube.com/watch?v=e_fpTvEcZxk

高中數學 向量內積的定義A
https://www.youtube.com/watch?v=7z9JrpSMJvs

高中數學 向量內積的定義B
https://www.youtube.com/watch?v=bfTWuqTFXlY

*高中數學 向量內積的性質
https://www.youtube.com/watch?v=cw-dAeAl9PY

*高中數學 向量內積的應用
https://www.youtube.com/watch?v=UQWOKsol2lI

*108新課綱 高二數學(上) 3-7【暖身】向量的內積
https://www.youtube.com/watch?v=x-oMK7g5JYk

*北一酷課師 高中數學 向量 10-4向量的內積定義與運算
https://www.youtube.com/watch?v=aA7iPCkpAmU

*EP.7 向量的內積｜第三冊 平面向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=b1bTysEhJG0

*EP.8 向量內積的性質｜第三冊 平面向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=jr1jsx2HsY0

*(更新)EP.9 正射影｜第三冊 平面向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=YwS-TPxFzzU

*EP.10 直線的參數式｜第三冊 平面向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=6mdWZjNfP54

*EP.11 兩線的夾角｜第三冊 平面向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=ml83pZX-v98

*EP.12 柯西不等式｜第三冊 平面向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=dKPVw_3xhMM

*平面向量的內積-正射影公式的說明
https://www.youtube.com/watch?v=ZzPlOfbib3E

*高中數學 向量正射影的應用與面積公式
https://www.youtube.com/watch?v=v8KgIAbpY_E

單元十向量(10-5)向量的正射影
https://www.youtube.com/watch?v=wiDk7WZbfOk

*【觀念】柯西不等式
https://www.youtube.com/watch?v=VvIe49As8A8

高中數學_平面向量_9.柯西不等式_葉政峯
https://www.youtube.com/watch?v=6r1TqxtKZWc

*北一酷課師 高中數學 向量 10 6柯西不等式與三角不等式
https://www.youtube.com/watch?v=bzbIoyA7Qvg

高中三大不等式之柯西不等式｜高二下第一次段考【三分鐘不負責任猜題】
https://www.youtube.com/watch?v=y5-dY8jo33g

柯西不等式
https://www.youtube.com/playlist?list=PLITtOb2Z4txyO-nOKtB_YWqiR8Zj_9Gxz

必考！正射影常考題｜高二下第一次段考【三分鐘不負責任猜題】
https://www.youtube.com/watch?v=nbFcCH9NTe0

【例題】求正射影長
https://www.youtube.com/watch?v=BmfvGHrc6hg

高中數學複習：平面向量-主題五（正射影）
https://www.youtube.com/watch?v=nzrRyIDKlG8

很簡單但常做不出來的向量內積問題
https://www.youtube.com/watch?v=gataQWw_D98

*【觀念】內積的定義（1／3）：物理上的作功
https://www.youtube.com/watch?v=Jv-qVF0vUmE

*【觀念】內積的定義（2／3）：數學上的內積
https://www.youtube.com/watch?v=bTrrRAabq4Y

*【觀念】內積的定義（3／3）：內積與角度
https://www.youtube.com/watch?v=7MhfelrqzzM

*The Vector Dot Product
https://www.youtube.com/watch?v=0iNrGpwZwog

*Dot Product of Two Vectors
https://www.youtube.com/watch?v=VzX8KJKFhlM

*內積與對偶 | 線性代數的本質 第七章
https://www.youtube.com/watch?v=LyGKycYT2v0

*Cross Product and Dot Product: Visual explanation
https://www.youtube.com/watch?v=h0NJK4mEIJU

*3D Dot Product (1 of 3: Foundational ideas)
https://www.youtube.com/watch?v=i3NdDvtmv80

*3D Dot Product (2 of 3: Deriving the formula for component form)
https://www.youtube.com/watch?v=PYaOSGDY1No

*3D Dot Product (3 of 3: Application to perpendicular vectors)
https://www.youtube.com/watch?v=CyXSZLElPpY

*Applications of Dot Products (1 of 2: Angles between vectors)
https://www.youtube.com/watch?v=l1ync-7UdX0

*Applications of Dot Products (2 of 2: Projections)
https://www.youtube.com/watch?v=ETXCx-wpBXY

*The meaning of the dot product | Linear algebra makes sense
https://www.youtube.com/watch?v=BcxfxvYCL1g

*Linear Algebra 20g: The Dot Product - One of the Most Brilliant Ideas in All of Linear Algebra
https://www.youtube.com/watch?v=QPkKWGq_V0U

*Linear Algebra 20h: The Key Properties of the Dot Product
https://www.youtube.com/watch?v=P_1yrghZhFw

*Inner Product is Dot Product, Turned on Its Head
https://www.youtube.com/watch?v=ZXOzKHq3-YA

*5.6 Vector Dot Product (Scalar Projection) - The Nature of Code
https://www.youtube.com/watch?v=DHPfoqiE4yQ

*Projections (1 of 4: Scalar projection)
https://www.youtube.com/watch?v=Tf-hx0n0YR4

*Projections (2 of 4: Vector projection)
https://www.youtube.com/watch?v=rlW7W0FTF3w

*Projections (3 of 4: Introductory example)
https://www.youtube.com/watch?v=wTp9qL_xH4s

*Projections (4 of 4: Further examples)
https://www.youtube.com/watch?v=ZtcUly_LxBE

*Inner Product for Complex Vector Spaces
https://www.youtube.com/watch?v=Kr3X1Pa9N3E

*Cauchy-Schwarz inequality
https://www.youtube.com/watch?v=TdcLxAYwrQI

*Proving the Cauchy–Schwarz Inequality for Vectors in R^n
https://www.youtube.com/watch?v=zaCMn5YVhVQ

*Vector triangle inequality | Vectors and spaces | Linear Algebra | Khan Academy
https://www.youtube.com/watch?v=PsNidCBr5II

*Proof of the Cauchy-Schwarz inequality | Vectors and spaces | Linear Algebra | Khan Academy
https://www.youtube.com/watch?v=r2PogGDl8_U

*Cauchy Schwarz Inequality I (visual proof)
https://www.youtube.com/watch?v=mKg_gVagHy8

*Functional Analysis - Part 10 - Cauchy-Schwarz Inequality
https://www.youtube.com/watch?v=4HOvKSPl6yM

*Cauchy Schwarz Inequality | Applications to Problems, and When Equality Occurs
https://www.youtube.com/watch?v=ZQm8qmQoKos

*Linear Algebra, Lesson 5, Video 16: Proof of Triangle Inequality
https://www.youtube.com/watch?v=tNF83h0CrAs

*Calculus III: The Dot Product (Level 12 of 12) | Cauchy-Schwarz, Triangle Inequality
https://www.youtube.com/watch?v=PekskOPTgJE

*22. The Cauchy-Schwarz Inequality
https://www.youtube.com/watch?v=7BI2bnn_57s