1. Vector Products

2. Vector Products (Cross Product) x z y i j k Physics 2048 Lecture Notesq x z y i j k
Physics 2048
Lecture Notes
Vector Products (Cross).ppt 2002

3. Cross Product (Vector Product)q A B C
Right Hand
Rule
Vector Products (Cross).ppt 2002

4. Cross Product h q |A x B| = |A| sin(q) |B| = h |B|
= area of Parallelogram
Vector Products (Cross).ppt 2002

5. Cross Product Using Unit Vectors y j i x z k
i x i = j x j = k x k = 0
i x j = k j x k = i k x i = j
j x i = -k k x j = -i i x k = -j
Vector Products (Cross).ppt 2002

6. Cross Product x z y i j k A = 2 i - 4 j + 6 k B = - i + 3 j - 5 k
A x B = (2 i - 4 j + 6 k) x (- i + 3 j - 5 k)
= 6(ixj) - 10(ixk) + 4(jxi) + 20(jxk) - 6(kxi) +18(kxJ)
k j k i j i
= ( ) i + (10 - 6) j + (6 - 4) k
A x B = 2 i + 4 j + 2 k
Vector Products (Cross).ppt 2002

7. Cross Product x z y i j k A = 7 i - 3 j B = 11 i + 8 j
A x B = (7 i - 3 j) x (11 i + 8 j)
= 7(8)(ixj) + 3(11)(jxi)
k k
= (56)k + (- 33) k
A x B = 23 k
Vector Products (Cross).ppt 2002

8. Cross Product x z y i j k A = 4 i + 2 j - k B = -3 i + 6 j - 2 k
A x B = (4 i + 2 j - k) x (-3 i + 6 j - 2 k)
= 24(ixj) - 8(ixk) - 6(jxi) - 4(jxk) + 3(kxi) - 6(kxJ)
k j k i j i
= (-4 + 6) i + (8 + 3) j + (24 + 6) k
A x B = 2 i + 11 j + 30 k
Vector Products (Cross).ppt 2002

9. Cross Product x z y i j k A = 5 i - j + 3 k B = 4 i - 6 j + 8 k
A x B = (5 i - j + 3 k) x (4 i - 6 j + 8 k)
= -30(ixj) + 40(ixk) - 4(jxi) - 8(jxk) +12(kxi) -18(kxJ)
k j k i j i
= (-8 +18) i + ( ) j + (30 +4) k
A x B = 10 i + 28 j - 26 k
Vector Products (Cross).ppt 2002

10. Vector Products Sample Problems Find Cross-Product A = 2 i + 2 j + 9 k
B = i - 6 j + 4 k
A x B = 62 i + j -14 k
Vector Products (Cross).ppt 2002

11. Vector Products Sample Problems Find Cross-Product A = 5 i + 8 j - 2 k
B = 7 i + 3 j + 7 k
A x B = 62 i - 49 j -41 k
Vector Products (Cross).ppt 2002

12. Vector Products Sample Problems Find Cross-Product
A = 4 i - 9 j + 10 k
B = 9 i + j + 3 k
A x B = - 37 i + 78 j + 85 k
Vector Products (Cross).ppt 2002

13. Vector Products Sample Problems Find Cross-Product A = 6 i + 5 j - 9 k
B = 10 i +7 j - 5 k
A x B = 31 i - 50 j - 8 k
Vector Products (Cross).ppt 2002

14. Vector Products Sample Problems Find Cross-Product A = 8 i + 5 j - 4 k
B = 11 i - 3 j + 7 k
A x B = 23 i j - 79 k
Vector Products (Cross).ppt 2002