Question

Answer whether true or false for all non-zero vectors a and b? ab=0⇒ a=0 or b=0.

Answer 1

The statement is FALSE. There are non-zero vectors a and b that satisfy the equation a * b = 0, but neither a nor b is equal to zero.

Step-by-step explanation:

In the given question, we are asked to determine whether the statement a * b = 0 ⇒ a = 0 or b = 0 is true for all non-zero vectors a and b.

The statement is FALSE. This is because there are non-zero vectors a and b that satisfy the equation a * b = 0, but neither a nor b is equal to zero.

For example, consider the vectors a = (1, 0, 0) and b = (0, 1, 0). The dot product of these vectors is a * b = 0. However, neither a nor b is equal to zero.