Question

If A = 6.0i - 8.0j units, B = -8.0i + 3.0j units and C = 26.0i + 19.0j units, determine a and b such that aA + bB + C = 0.

a. a = 2, b = -3
b. a = -3, b = 2
c. a = 3, b = -2
d. a = -2, b = 3

Answer 1

By setting up and solving a system of linear equations for the i and j components, we determine that the correct values for a and b such that aA + bB + C = 0 are a = -2 and b = 3, which corresponds to option d.

Step-by-step explanation:

To find values of a and b such that aA + bB + C = 0 where A = 6.0i - 8.0j units, B = -8.0i + 3.0j units, and C = 26.0i + 19.0j units, we can set up a system of linear equations based on the i and j components.

For the i-component:

6.0a - 8.0b + 26.0 = 0

For the j-component:

-8.0a + 3.0b + 19.0 = 0

Solving this system of equations yields a = -2 and b = 3.

Therefore, the correct answer is option d: a = -2, b = 3.