- A$\overrightarrow {OA} + \overrightarrow {OB} - \overrightarrow {OC} $
- B$\overrightarrow {OA} + \overrightarrow {OB} - \overrightarrow {BD} $
- ✓$\overrightarrow {OA} + \overrightarrow {OB} + \overrightarrow {OC} $
- DNone of these
$ = \overrightarrow {OD} + \overrightarrow {DA} + \overrightarrow {OD} + \overrightarrow {DB} + \overrightarrow {OD} + \overrightarrow {DC} $$ = \overrightarrow {OA} + \overrightarrow {OB} + \overrightarrow {OC} .$
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($A$) There exists an $\mathrm{h} \in\left[\frac{1}{4}, \frac{2}{3}\right]$ such that the area of the green region above the line $\mathrm{L}_{\mathrm{h}}$ equals the area of the green region below the line $\mathrm{L}_{\mathrm{h}}$
($B$) There exists an $\mathrm{h} \in\left[\frac{1}{4}, \frac{2}{3}\right]$ such that the area of the red region above the line $\mathrm{L}_{\mathrm{h}}$ equals the area of the red region below the line $\mathrm{L}_h$
($C$) There exists an $\mathrm{h} \in\left[\frac{1}{4}, \frac{2}{3}\right]$ such that the area of the green region above the line $\mathrm{L}_{\mathrm{h}}$ equals the area of the red region below the line $L_h$
($D$) There exists an $\mathrm{h} \in\left[\frac{1}{4}, \frac{2}{3}\right]$ such that the area of the red region above the line $\mathrm{L}_{\mathrm{h}}$ equals the area of the green region below the line $\mathrm{L}_{\mathrm{h}}$