Let the three sides of a triangle ABC be given by the vectors 2i-j+k, i-3j-5k and 3i-4j-4k. Let G be the centroid of the triangle ABC. Then 6 (|AG|²+|BG|²+|CG|²) is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q125

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

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\bigl(|\overrightarrow{AG}|^2+|\overrightarrow{BG}|^2+|\overrightarrow{CG}|^2\bigr)

is equal to:

Your answerInteger or decimal