Three forces act on an object with

F1 = (6.03i + 11.17j) N
and
F2 = (2.19i − 13.53j) N.
If the net force on the object is zero, what is the unknown force,
F3?
(Express your answer in vector form.)
F3 =
N

Let's take F3 as (xi + yj)N

The sum along each component of all three force vectors is zero, so:

(6.03 + 2.19 + x)i = (0)i
=> 8.22 + x = 0
=> x = -8.22

(11.17 - 13.53 + y)j = (0)j
=> -2.36 + y = 0
=> y = 2.36

So, F3 is given by (-8.22i + 2.36)N

F1 + F2 = (6.03i+11.17j)+(2.19i-13.53j) = (8.22i - 2.36j.

F3 = -(F1+F2) = -(8.22i-2.36j) = -8.22i + 2.36j.

To find the unknown force F3, we need to calculate the negative sum of the first two forces F1 and F2.

F3 = - (F1 + F2)

First, we add the corresponding components of F1 and F2:

F1 + F2 = (6.03i + 11.17j) + (2.19i - 13.53j)

Simplifying the expression, we get:

F1 + F2 = (6.03 + 2.19)i + (11.17 - 13.53)j
= 8.22i - 2.36j

Finally, we multiply the result by -1 to get the negative sum:

F3 = -(8.22i - 2.36j)
= -8.22i + 2.36j

Therefore, the unknown force F3 is equal to -8.22i + 2.36j N.

To find the unknown force, F3, we need to calculate the sum of the first two forces, F1 and F2, and then subtract it from zero to get the net force equal to zero.

Step 1: Calculate the sum of the two given forces, F1 and F2:
F1 = (6.03i + 11.17j) N
F2 = (2.19i − 13.53j) N

Add the corresponding components of the forces:
F1 + F2 = (6.03i + 11.17j) N + (2.19i − 13.53j) N
= (6.03i + 2.19i) N + (11.17j - 13.53j) N
= 8.22i - 2.36j N

Step 2: Subtract the sum of the forces from zero to find F3:
F3 = - (F1 + F2)
= - (8.22i - 2.36j) N
= -8.22i + 2.36j N

Therefore, the unknown force, F3, is equal to -8.22i + 2.36j N in vector form.