Let the position vectors of the vertices A, B and C of a triangle be 2 i+2 j+k, i+2 j+2 k and 2 i+j+2 k respectively. Let l₁, l₂ and l₃ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides AB, BC and CA respectively, then l₁²+l₂²+l₃² equals:

Vector Algebra: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Evening shift · Q5845

JEE Main 202427 Jan, Evening shiftMathematicsHardVector Algebra184× since 2002

Let the position vectors of the vertices

\mathrm{A}, \mathrm{B}

and

\mathrm{C}

of a triangle be

2 \hat{i}+2 \hat{j}+\hat{k}, \hat{i}+2 \hat{j}+2 \hat{k}

and

2 \hat{i}+\hat{j}+2 \hat{k}

respectively. Let

l_1, l_2

and

l_3

be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides

\mathrm{AB}, \mathrm{BC}

and

\mathrm{CA}

respectively, then

l_1^2+l_2^2+l_3^2

equals: