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Mr. One is pushing a cart with a force of F1 = 15.00 N due north. Mr. Two is pushing the same cart with a force of F2 = 25.00 N due northeast. Mr. Three is pushing the cart a force F3 so that the cart is in equilibrium. Find force F3 so that . First, we calculate the vector sum  by component method. The x-component of  is  and the y-component is  . The x-component of  is  and the y-component is  . Adding the components, we can express the resultant vector in unit vector component form:  =   +   Since we want to find , it follows that . Thus,  =   +    The magnitude of  is F3 =  N.

Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed.

Mr. One is pushing a cart with a force of F1 = 15.00 N due north. Mr. Two is pushing the same cart with a force of F2 = 25.00 N due northeast. Mr. Three is pushing the cart a force F3 so that the cart is in equilibrium. Find force F3 so that .

First, we calculate the vector sum  by component method.

The x-component of  is  and the y-component is  .

The x-component of  is  and the y-component is  .

Adding the components, we can express the resultant vector in unit vector component form:

=   +

Since we want to find , it follows that . Thus,

=   +

The magnitude of  is F3 =  N.

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