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Mathematics 1
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səhifə | 4/5 | tarix | 26.10.2023 | ölçüsü | 1,08 Mb. | | #131170 |
| Vectorsa × b = 0 a × b = −b × a - the vector product is anti-commutative (a) × b = (a × b) = a × (b)- Scalar Multiplication Property a × (b + c) = a × b + a × c –distributive property (a + b) × c = a × c + b × c
Vector Product in terms of vectors’ components - For two vectors a and b defined by their components
- a( a1;a2;a3) and b( b1;b2;b3) the cross product is given by the formula:
- Easy to memorise using the fact that the cross product is really the determinant of a 3x3 matrix:
The Method of Cofactors to calculate:
where,
Vector Product in terms of vectors’ components -2D - Two 2D vectors a and b can be defined by their components as a special case:
- a( a1;a2;0) and b( b1;b2;0), then the matrix for the cross product:
==-+= == (- Then = =
Vector Product in terms of vectors’ components - The second method is easier but it will only work on 3x3 determinants
- .
- =a2b3+a3b1 +a1b2 -a1b3 -a3b2-a2b1 =(a2b3-a3b2)+ (a3b1- a1b3)+ (a1b2- a2b1)
- If = (2;1;-1) and =(-3;4;1)compute each of the following:
- 1) 2)
- Solution:
1)
2)
- We can give a geometrical interpretation to the magnitude of the vector product if we consider the parallelogram below.
- The area of this parallelogram is
product: - Area = base × height = h =
sin() = -
h= v
Dostları ilə paylaş: |
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