Question

Which of the following statements are always true for vectors in R3?

a. If u · (v × w) = 4 then w · (u × v) = −4
b. (2u + v) × (u + 7v) = 13 (u × v)

Answer 1

The statements provided are not always true for vectors in R3.

Step-by-step explanation:

To determine the statements that are always true for vectors in R3, let's analyze each statement:

a. If u · (v × w) = 4, then w · (u × v) = −4

This statement is not always true. The dot product is not commutative, so u · (v × w) is not equal to w · (u × v)

b. (2u + v) × (u + 7v) = 13(u × v)

This statement is not always true. The cross product does not distribute over addition, so (2u + v) × (u + 7v) is not equal to 13(u × v)