Let the position vectors of the vertices A, B and C of a triangle be 2î + 2ĵ + k̂, î + 2ĵ + 2k̂ and 2î + ĵ + 2k̂ 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 \(ℓ_1^2 + ℓ_2^2 + ℓ_3^2\) equals :
1
\(\frac{1}{5}\)
2
\(\frac{1}{2}\)
3
\(\frac{1}{4}\)
4
\(\frac{1}{3}\)