1.2 - Math Review

Cross Product • Cross (vector) product of two vectors gives you a vector perpendicular to both whose magnitude is equal to the area of a parallelogram defined by the two initial vectors • Positive direction of the cross product is given by the right-hand rule • Cross product of parallel vectors is zero. Calculating the Cross Product • |A ⃗×B ⃗ |=AB sin⁡θ • A ⃗×B ⃗=|■8(i ̂&j ̂&k ̂@A_x&A_y&A_z@B_x&B_y&B_z )|=(A_y B_z−A_z B_y ) i ̂+(A_z B_x−A_x B_z ) j ̂+(A_x B_y−A_y B_x ) k ̂ Cross Product Properties • A ⃗×B ⃗=−B ⃗×A ⃗ • A ⃗×(B ⃗+C ⃗ )=A ⃗×B ⃗+A ⃗×C ⃗ • c(A ⃗×B ⃗ )=(cA ⃗ )×B ⃗=A ⃗×(cB ⃗ ) • d/dt (A ⃗×B ⃗ )=(dA ⃗)/dt×B ⃗+A ⃗×(dB ⃗)/dt Unites