mcv4u1 5.4 - the cross product of two vectors the cross product also called a "vector...
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MCV4U1
5.4 - The Cross Product Of Two Vectors
The cross product also called a "vector product" only exists in R3. a CROSS b, produces a vector quantity that is perpendicular to BOTH a and b.
If a = (x1, y1, z1) and b = (x2, y2, z2)
Cross Product Formula:
=(y1z2 - y2z1, z1x2 - z2x1, x1y2 - x2y1)
a
ba x b
Cross Product Shortcut!!!
Instead of memorizing the formula for the cross product try usingthe following shortcut.
1.) Eliminate (ignore) the component column that you are trying to calculate.
2.) Calculate: Down Product - Up Product.
= x1 y1 z1 x1
x2 y2 z2 x2
=(y1z2 - y2z1, z1x2 - z2x1, x1y2 - x2y1)
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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