Question

A force vector →A has x- and y-components, respectively, of −8.80 units of force and 15.00 units of force. The x- and y-components of force vector →B are, respectively, 13.20 units of force and −6.60 units of force. Find the components of force vector →C that satisfies the vector equation →A−→B+3→C=0.

a) →C: (4.00, 5.00)
b) →C: (-4.00, -5.00)
c) →C: (-2.00, -1.00)
d) →C: (2.00, 1.00)

Answer 1

The components of force vector C that satisfy the vector equation A - B + 3C = 0 are C: (4.00, 5.00).

Step-by-step explanation:

To find vector C that satisfies the equation A - B + 3C = 0, we need to solve for the components of vector C. Let's break down the equation and solve it piece by piece.

The x-component of vector A is -8.80 units of force, the x-component of vector B is 13.20 units of force, and the x-component of vector C is x. Plugging these values into the equation, we get:

-8.80 - 13.20 + 3x = 0

Simplifying this equation, we find: x = 4.00

Similarly, the y-component of vector A is 15.00 units of force, the y-component of vector B is -6.60 units of force, and the y-component of vector C is y. Plugging these values into the equation, we get:

15.00 - (-6.60) + 3y = 0

Simplifying this equation, we find: y = 5.00

Therefore, the components of vector C that satisfy the equation are C: (4.00, 5.00).