Question

If a = <4, 0, 4 >, b =< 3, 4, −4 >, and c = <0, 4, 4> , show that a ⨯ (b ⨯ c) ≠ (a ⨯ b) ⨯ c. a ⨯ (b ⨯c)

Answer 1

To show that a ⨯ (b ⨯ c) ≠ (a ⨯ b) ⨯ c, we can calculate both sides of the equation and compare the results.

Step-by-step explanation:

To show that a ⨯ (b ⨯ c) ≠ (a ⨯ b) ⨯ c, we can calculate both sides of the equation and compare the results. Let's start with the left side, a ⨯ (b ⨯ c):

1. Calculate the cross product of b and c: b ⨯ c = -44, 12, 16
2. Calculate the cross product of a and the result from step 1: a ⨯ (b ⨯ c) = 0, 16, -12

Next, let's calculate the right side, (a ⨯ b) ⨯ c:

1. Calculate the cross product of a and b: a ⨯ b = -16, 16, 16
2. Calculate the cross product of the result from step 1 and c: (a ⨯ b) ⨯ c = -32, -48, -80

As we can see, a ⨯ (b ⨯ c) is not equal to (a ⨯ b) ⨯ c, since the two sides yield different results.