JEE Mains · Maths · STD 12 - 10. vector algebra
Let the three sides of a triangle \(A B C\) be given by the vectors \(2 \hat{i}-\hat{j}+\hat{k}, \quad \hat{i}-3 \hat{j}-5 \hat{k}\) and \(3 \hat{i}-4 \hat{j}-4 \hat{k}\). Let \(G\) be the centroid of the triangle \(A B C\). Then \(6\left(|\overrightarrow{\mathrm{AG}}|^2+|\overrightarrow{\mathrm{BG}}|^2+|\overrightarrow{\mathrm{CG}}|^2\right)\) is equal to ________
- A 162
- B 164
- C 160
- D 158
Answer & Solution
Correct Answer
(B) 164
Step-by-step Solution
Detailed explanation
By given data \(\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}=\overrightarrow{\mathrm{CB}}\) Let pv of \(\overrightarrow{\mathrm{A}}\) are \(\overrightarrow{\mathrm{O}}\) then \(\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{A}}\)…
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