\overline{i}+\overline{j}+\overline{k}, a_1 \overline{i}+b_1 \overline{j}+c_1 \overline{k}, a_2 \overline{i}+b_2 \overline{j}+c_2 \overline{k}, a_3 \overline{i}+b_3 \overline{j}+c_3 \overline{k} are the position vectors of the points {\A}, {\B}, {\C}, {\D} respectively. \frac{2}{3}(\overline{i}+\overline{j}+\overline{k}) is the position vector of the centroid of the triangular face BCD of the tetrahedron ABCD . If \alpha \overline{i}+\beta \overline{j}+\gamma \overline{k} is the position vector of the centroid of the tetrahedron, then 2 \alpha+\beta+\gamma=

TG EAMCET 3 May 2025 Shift 2 Paper

Question : 31 of 160

Marks: +1, -0

i+j+k,a1i+b1j+c1k,a2i+b2j+c2k,a3i+b3j+c3k are the position vectors of the points A,B,C,D respectively. ‌

(i+j+k) is the position vector of the centroid of the triangular face BCD of the tetrahedron ABCD . If αi+βj+γk is the position vector of the centroid of the tetrahedron, then 2α+β+γ=

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