Triangle Sides Centroid Vector Sum (Jee Mains)

Vector Algebra and Components

Medium

Triangle Sides Centroid Vector Sum

Let the three sides of a triangle ABC be given by the vectors $2\hat i - \hat j + \hat k$ , $\hat i - 3\hat j - 5\hat k$ and $3\hat i - 4\hat j - 4\hat k$ . Let G be the centroid of the triangle ABC. Then $6\left( {{{\left| {\overrightarrow {AG} } \right|}^2} + {{\left| {\overrightarrow {BG} } \right|}^2} + {{\left| {\overrightarrow {CG} } \right|}^2}} \right)$ is equal to ____

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