Question

Given a = (4, -3) and b = (2, -1), find a + 3b.

A) (14, -6)

B) (8, 0)

C) (10, -6)

Answer 1

To calculate a + 3b, multiply vector b by 3 and add it to vector a. The result of adding vector a = (4, -3) to 3 × vector b = (6, -3) is the vector (10, -6).

Step-by-step explanation:

To find the vector a + 3b, we first multiply the vector b by 3 and then add it to vector a. The vector b is given as (2, -1), so 3b is (3 × 2, 3 × -1), which equals (6, -3). Now, we add a, which is (4, -3), to the newly found 3b to get the resulting vector.

a + 3b = (4, -3) + (6, -3) = (4 + 6, -3 - 3) = (10, -6).

Therefore, the correct answer is C) (10, -6).