MCV4U The Cross Product Of Two Vectors The cross product also called a "vector product" only exists in R 3. a CROSS b, produces a vector quantity that is perpendicular to BOTH a and b. If a = (x 1, y 1, z 1 ) and b = (x 2, y 2, z 2 ) Cross Product Formula: =(y 1 z 2 - y 2 z 1, z 1 x 2 - z 2 x 1, x 1 y 2 - x 2 y 1 ) a b a x b

Cross Product Shortcut!!! Instead of memorizing the formula for the cross product try using the following shortcut. 1.) Eliminate (ignore) the component column that you are trying to calculate. 2.) Calculate: Down Product - Up Product. =x1y1z1x1x2y2z2x2=x1y1z1x1x2y2z2x2 =(y 1 z 2 - y 2 z 1, z 1 x 2 - z 2 x 1, x 1 y 2 - x 2 y 1 )

Ex.) Calculate the cross product of the following pairs of vectors. a) a = (6, -1, 3) and b = (-2, 5, 4) b) u = (4, -6, 7) and v = (1, 3, 2)

Magnitude of the cross product * Where θ is the angle between the vectors Ex.) If and the angle between them is 30 find

Ex.) If a = (3, -1, -5) and b = ( 7, -3, 0) find: a) b) c) A unit vector perpendicular to BOTH a and b.

Properties of the Cross Product 1) Commutative Law is NOT true. 2) Distributive Property 3) Scalar Multiplication 4) However AND

Homework: p.185 # 1 - 7, 9, 15

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