Question

Find vectors A, B, C, D which satisfy the following conditions: A ≠ B but (A) = (B); C ≠ D but (C) = (D); (A) ≠ (C).

a) A = (1, 2), B = (2, 3), C = (3, 4), D = (4, 5)
b) A = (1, 2), B = (1, 2), C = (3, 4), D = (3, 4)
c) A = (1, 2), B = (1, 2), C = (1, 2), D = (3, 4)
d) A = (1, 2), B = (3, 4), C = (1, 2), D = (3, 4)

Answer 1

The order of addition of three vectors does not affect their sum. This property can be shown by adding three vectors in different orders and observing that the sum remains the same.

Step-by-step explanation:

When adding vectors, the order of addition does not affect the sum. To show this, let's choose three vectors A, B, and C, each with different lengths and directions. Let's find the sum A + B + C and then find their sum when added in a different order. For example, let A = (2, 3), B = (4, 5), and C = (6, 7).

Sum of A + B + C = (2, 3) + (4, 5) + (6, 7) = (12, 15).

Let's change the order now: Sum of B + A + C = (4, 5) + (2, 3) + (6, 7) = (12, 15).

As you can see, regardless of the order of addition, the sum remains the same.