8 2.3 the Cartesian representation of any vector Unit(basis) vectors: i,j, k Magnitudes: 1 Directions: indicate the directions that correspond coordinates Increase Scalar product of the Cartesian unit vectors with each other =0.k 0 11=0 0k.=0k.k=1 8 2.3 the Cartesian representation of any vector 2. The case of two dimensions A A.i+4 Acos bi+asin e Ⅴ ector a gnitude:A=A2+A2 Direction: decided by angle e=tan A5 §2.3 the Cartesian representation of any vector Unit(basis) vectors: i j k ˆ ,ˆ ,ˆ Magnitudes: 1 Directions: indicate the directions that correspond coordinates increase. i ˆ k ˆ j ˆ x y z 1 ˆ ˆ i ⋅ i = 0 ˆ ˆ i ⋅ j = 0 ˆ ˆ i ⋅ k = 0 ˆ ˆ j ⋅ i = 1 ˆ ˆ j ⋅ j = 0 ˆ ˆ j ⋅ k = 0 ˆ ˆ k ⋅ i = 0 ˆ ˆ k ⋅ j = 1 ˆ ˆ k ⋅ k = Scalar product of the Cartesian unit vectors with each other §2.3 the Cartesian representation of any vector 2. The case of two dimensions A i A j A A i A j x y ˆ sin ˆ cos ˆ ˆ = θ + θ = + r A r Ax Ay x y i ˆ j ˆ θ Vector A r Magnitude: 2 2 A = Ax + Ay Direction: decided by angle x y A 1 A tan− θ =