3overrightarrow{OD} + overrightarrow{DA} + ov | vedclass

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Question

(C) Given expression: $3\overrightarrow{OD} + \overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC}$We can rewrite the expression by splitti

Vedclass · Accepted Answer

$\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC}$

Vedclass · Answer

(C) Given expression: $3\overrightarrow{OD} + \overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC}$We can rewrite the expression by splitting $3\overrightarrow{OD}$ into three parts:$= \overrightarrow{OD} + \overrightarrow{DA} + \overrightarrow{OD} + \overrightarrow{DB} + \overrightarrow{OD} + \overrightarrow{DC}$Using the triangle law of vector addition,$\overrightarrow{OX} + \overrightarrow{XY} = \overrightarrow{OY}$:$\overrightarrow{OD} + \overrightarrow{DA} = \overrightarrow{OA}$$\overrightarrow{OD} + \overrightarrow{DB} = \overrightarrow{OB}$$\overrightarrow{OD} + \overrightarrow{DC} = \overrightarrow{OC}$Substituting these into the expression:$= \overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC}$Thus,the correct option is $C$.

$3\overrightarrow{OD} + \overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC} = $

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