InterviewSolution
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InterviewSolution
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If `P`is any arbitrary point onthe circumcirlce of the equllateral trangle of side length `l`units, then `| vec P A|^2+| vec P B|^2+| vec P C|^2`is always equal to`2l^2`b. `2sqrt(3)l^2`c. `l^2`d. `3l^2`A. `2l^(2)`B. `2sqrt3l^(2)`C. `l^(2)`D. `3l^(2)` |
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Answer» Correct Answer - a Let P.V. of A,B and C be `vecp, veca, vecb and vecc` respectively, and `O(vec0)` be the circumcentre of equilateral traingle ABC. Then `|vecP| = |vecb| = |veca|= |vecc| = l/ sqrt3` Now `|vec(PA)|^(2) = |veca - vecp|^(2)= |veca|^(2) + |vecp|^(2) - 2vecp` ` and |vecPC|^(2) = |vecc|^(2) + |vecp|^(2) - 2vecp. vecc` ` Rightarrow sum|vec(PA)|^(2) = 6. l^(2)/3 - 2vecp . (veca + vecb + vecc)` ` 2l^(2) (as veca + vecb + vecc//3 = vec0)` |
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