Question

Given the vectors a = (-9, -5) and b = (6, -3), find 9a and a - b. Write your answers in component form.

A) 9a = (-81, -45) and a - b = (-15, -2)
B) 9a = (-54, -27) and a - b = (-15, -2)
C) 9a = (-81, -45) and a - b = (-3, -2)
D) 9a = (-54, -27) and a - b = (-3, -2)

Answer 1

The vector 9a is calculated by multiplying each component of vector a by 9, resulting in (-81, -45). The vector a - b is found by adding the negative of vector b to vector a, yielding (-15, -2). The correct answer is Option A.

Step-by-step explanation:

To find 9a, we multiply each component of vector a by 9.

• 9 × (-9) = -81
• 9 × (-5) = -45

Therefore, 9a = (-81, -45).

When subtracting vector b from vector a (a - b), we add the negative of vector b to vector a. We find the components of the resultant vector R by:

• Rx = Ax + (-Bx) = -9 + (-6) = -15
• Ry = Ay + (-By) = -5 + 3 = -2

So, a - b = (-15, -2).

Combining these results, we have 9a = (-81, -45) and a - b = (-15, -2).