If $A,B,C,D,E$ are five coplanar points, then $\overrightarrow{\mathbf{DA}}\mathbf{+}\overrightarrow{\mathbf{DB}}\mathbf{+}\overrightarrow{\mathbf{DC}}\mathbf{+}\overrightarrow{\mathbf{AE}}\mathbf{+}\overrightarrow{\mathbf{BE}}\mathbf{+}\overrightarrow{\mathbf{CE}}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
$\overrightarrow{\mathbf{DA}}\mathbf{+}\overrightarrow{\mathbf{DB}}\mathbf{+}\overrightarrow{\mathbf{DC}}\mathbf{+}\overrightarrow{\mathbf{AE}}\mathbf{+}\overrightarrow{\mathbf{BE}}\mathbf{+}\overrightarrow{\mathbf{CE}}$
$\mathbf{=}\left( \mathbf{\ }\overrightarrow{\mathbf{DA}}\mathbf{+}\overrightarrow{\mathbf{AE}}\mathbf{\ } \right)\mathbf{+}\left( \overrightarrow{\mathbf{DB}}\mathbf{+}\overrightarrow{\mathbf{BE}}\mathbf{\ } \right)\mathbf{+}\left( \overrightarrow{\mathbf{DC}}\mathbf{+}\overrightarrow{\mathbf{CE}}\mathbf{\ } \right)$
$\mathbf{=}\overrightarrow{\mathbf{DE}}\mathbf{+}\overrightarrow{\mathbf{DE}}\mathbf{+}\overrightarrow{\mathbf{DE}}$
$= 3\ \overrightarrow{\mathbf{DE}}$

Q. If $A,B,C,D,E$ are five coplanar points, then $\overrightarrow{\mathbf{DA}}\mathbf{+}\overrightarrow{\mathbf{DB}}\mathbf{+}\overrightarrow{\mathbf{DC}}\mathbf{+}\overrightarrow{\mathbf{AE}}\mathbf{+}\overrightarrow{\mathbf{BE}}\mathbf{+}\overrightarrow{\mathbf{CE}}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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