1.6: Determinants and Cross Product

Question 1

How does A x B relate to A and B?

Answer 1

A x B is orthogonal/perpendicular to BOTH A and B

Question 2

What is |A x B| equal to?

Answer 2

|A||B|sinθ

Question 3

Is A x B communicative? (Does A x B = B x A?)

Answer 3

NO, A x B = - B x A

Question 4

What are ways you can distribute a constant with the cross product?

Answer 4

(cA) x B = A x (cB) = c(A x B)

Question 5

What’s another way to write A x (B + C)?

Answer 5

(A x B) + (A x C)

Question 6

How else to write A • (B x C)?

Answer 6

(A x B) • C

Question 7

How can you rewrite the following WITHOUT using the cross product?
A x (B x C)

Answer 7

(A•C)B - (A•B)C

[NOTE: this is NOT (A•B)•C because you can’t do the dot product between a scalar and a vector, (A•B)C is multiplying a vector by a scalar]

Question 8

What is a determinant?

Answer 8

the solution you get from solving a 3x3 matrix?? (Idk if that’s right)

Question 9

Do the vectors A, B, and A x B follow the right hand rule?

Answer 9

Yes

Question 10

If A x B = 0, what does that tell you?

Answer 10

If A x B = 0, then A and B are parallel
(Also: if A and B are parallel, then A x B = 0(

Question 11

_______ is equal to the area of the parallelogram generated by A and B

Answer 11

|A x B|

Question 12

What is the volume of the parallelpiped generated by A, B, and C equal to?

Answer 12

|A•(B x C)|

Question 13

What’s a faster way to calculate A•(B x C)?

Answer 13

|a1 a2 a3|
|b1 b2 b3|
|c1 c2 c3|