Vector Products.

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Presentation transcript:

Vector Products

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

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

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

Cross Product Using Unit Vectors y j i x z k i x i = 0 j x j = 0 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

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 = (20 - 18) i + (10 - 6) j + (6 - 4) k A x B = 2 i + 4 j + 2 k Vector Products (Cross).ppt 2002

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

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

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 + (-40 +12) j + (30 +4) k A x B = 10 i + 28 j - 26 k Vector Products (Cross).ppt 2002

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

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

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

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

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 - 100 j - 79 k Vector Products (Cross).ppt 2002

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