Chapter 0 Preface A·B=B.A AA=A Prove it? A(B+C)=A·B+AC A=A2+4+Ak) A·B=? B=Bi+Bj+Bk A·B=(A1i+A1j+Ak)·(B,i+B,j+Bk) AB+AB+aB AB=AB+A,B+A
Chapter 1Chapter 1 Measurment Chapter 0 Preface A A i A j A k x y z = + + B B i B j B k x y z = + + AB = ? A B (A i A j A k) (B i B j B k) x y z x y z = + + + + = Ax Bx + Ay By + Az Bz A B = Ax Bx + Ay By + Az Bz A B B A = 2 2 A A = A| = A | A B C A B A C ( + ) = + Prove it?
Chapter 0 Preface 3. 2)Cross product: AxB= ABsin(e)n The length of A X B can be interpreted as the area of the parallelogram having A and B as sides n is a unit vector perpendicular to both a and B A,B, and n also becomes a right handed system. AxBb≤兀 AB,A×B=0 B A⊥B,|AxB=AB 0 Scalar triple product A(B×C) B×A=-4×B
Chapter 1Chapter 1 Measurment Chapter 0 Preface 3.2) Cross product: A B ABsin n = () is a unit vector perpendicular to both and . , , and also becomes n a right handed system. n The length of × can be interpreted as the area of the parallelogram having A and B as sides. A B A B A B A B A B n B A -A B = θ If A B,| A B| AB If A//B, A B 0 ⊥ = = Scalar triple product: A(BC) = ?
Chapter 0 Preface A=Ai+A,j+Ak A×B=? B=Bi+Bi+Bk A×B=(41i+A+A)×(B1+B,j+B2k) (A, B.-AB)i+(AB-AB).j +(ABy-A B k 7k|=(A,B:-AB,)元 A×B=A.A,A +(A B-A B.j Br By B+(ABy-A, B)k
Chapter 1Chapter 1 Measurment Chapter 0 Preface A A i A j A k x y z = + + B B i B j B k x y z = + + A B = ? A B (A i A j A k) (B i B j B k) x y z x y z = + + + + A B A B i A B A B j y z z y z x x z = ( − ) + ( − ) A B A B k x y y x + ( − ) x y z x y z B B B A A A i j k A B = A B A B j z x x z + ( − ) A B A B k x y y x + ( − ) A B A B i y z z y = ( − )