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Vector Algebra question

2024 · 4 Apr · Shift 1 · Q59

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JEE Main
Mathematics
Vector Algebra
2024 · 4 Apr · Shift 1 · Q59

Vector Algebra question

2024 · 4 Apr · Shift 1 · Q59

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

\mathrm{ABC}

be a triangle of area

15 \sqrt{2}

and the vectors

\overrightarrow{\mathrm{AB}}=\hat{i}+2 \hat{j}-7 \hat{k}, \overrightarrow{\mathrm{BC}}=\mathrm{a} \hat{i}+\mathrm{b} \hat{j}+\mathrm{c} \hat{k}

and

\overrightarrow{\mathrm{AC}}=6 \hat{i}+\mathrm{d} \hat{j}-2 \hat{k}, \mathrm{~d}\gt 0

. Then the square of the length of the largest side of the triangle

\mathrm{ABC}

is

\underline{\hspace{2cm}}

.

Numerical answer

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