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(C) From the figure,the force $\vec{F}$ makes an angle of $45^{\circ}$ with the positive $x$-axis in the fourth quadrant.Therefore,the angle with the

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$50\sqrt{2}\,(\hat{i} - \hat{j})$

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(C) From the figure,the force $\vec{F}$ makes an angle of $45^{\circ}$ with the positive $x$-axis in the fourth quadrant.Therefore,the angle with the positive $x$-axis is $	heta = -45^{\circ}$.The components of the force are:$F_x = F \cos(-45^{\circ}) = 100 	imes \frac{1}{\sqrt{2}} = 50\sqrt{2}$$F_y = F \sin(-45^{\circ}) = 100 	imes \left(-\frac{1}{\sqrt{2}}ight) = -50\sqrt{2}$Thus,the force in unit vector notation is:$\vec{F} = F_x \hat{i} + F_y \hat{j} = 50\sqrt{2} \hat{i} - 50\sqrt{2} \hat{j} = 50\sqrt{2}(\hat{i} - \hat{j})$

$A$ person pushes a box kept on a horizontal surface with a force of $100\,N$ as shown in the figure. In unit vector notation,the force $\vec{F}$ can be expressed as?

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