Let ABC be a triangle of area 15 √(2) and the vectors AB=i+2 j-7 k, BC=a i+b j+c k and AC=6 i+d j-2 k, ~d>0. Then the square of the length of the largest side of the triangle ABC is _ _ _ _ _.

Vector Algebra: JEE Main 2024 Mathematics question

JEE Main 2024 · 4 Apr, Morning shift · Q53

JEE Main 20244 Apr, Morning shiftMathematicsHardVector Algebra184× since 2002

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}>0

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

\mathrm{ABC}

is _________.

Your answerType your answer. Integers and decimals are accepted.