1 Chalkboard
Figure 1: Cross product of 2 vectors in 3-space
Figure 2: Area of parallelogram with cross product
Figure 3: Right hand method for direction of cross product
Figure 4: Another look at volume
Figure 5: Volume of parallelopiped
Figure 6: Review of cross product
Figure 7: Inverse direction of cross product
2 Can we use the commutivity law with cross product?
2.1 Front
Can we use the commutivity law with cross product?
\(\vb{A} \cross \vb{B} = \vb{B} \cross \vb{A}\)
2.2 Back
Not it’s not equivalent, but we can say that \(\vb{A} \cross \vb{B} = - \vb{B} \cross \vb{A}\)
3 What we can say of \(\vb{a} \cross \vb{a}\)
3.1 Front
What we can say of $\vb{a} \cross \vb{a}$
3.2 Back
- \(\vb{a} \cross \vb{a} = 0\)
- There is no area between the same vector
4 Can we apply distributive law to cross product?
4.1 Front
Can we apply distributive law to cross product?
\(\vb{A} \cross (\vb{B} + \vb{C}) = \vb{A} \cross \vb{B} + \vb{A} \cross \vb{B}\)
4.2 Back
Yes
5 Can we use associativity law to cross product?
5.1 Front
Can we use associativity law to cross product?
\((\vb{A} \cross \vb{B}) \cross \vb{C} = \vb{A} \cross (\vb{B} \cross \vb{C})\)
5.2 Back
No, you can test with unit vectors \(\hat{i}, \hat{j}, \hat{k}\)