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Vector Algebra question

2025 · 4 Apr · Shift 2 · Q48

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JEE Main
Mathematics
Vector Algebra
2025 · 4 Apr · Shift 2 · Q48

Vector Algebra question

2025 · 4 Apr · Shift 2 · Q48

JEE MainMathematicsVector AlgebraNumerical+4 / −1

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

A B C

. Then

6\left(|\overrightarrow{\mathrm{AG}}|^2+|\overrightarrow{\mathrm{BG}}|^2+|\overrightarrow{\mathrm{CG}}|^2\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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