InterviewSolution
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InterviewSolution
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If a, b and c are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of `|a+b+c|^(2)` isA. `|a|^(2)+|b|^(2)+|c|^(2)`B. `|a|+|b|+|c|`C. `2 (|a|^(2)+|b|^(2)+|c|^(2))`D. `1/2 (|a|^(2)+|b|^(2)+|c|^(2))` |
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Answer» Correct Answer - A According to the given condition, each vectors is perpendicular to the sum of the vectors. `:. a.(b+c) =0`, `b.(a+c) =0` and `c.(a+b) = 0` `rArr a.b+a.c = 0, b.a + b.c = 0` and `c.a + c.b = 0` `rArr 2(a.b+b.c +c.a) = 0` `rArr a.b+b.c+c.a= 0"...."(i)` Now, `|a+b+c|^(2) = |a|^(2) + |b|^(2) + |c|^(2) + 2(a.b+b.c+c.a)` `= |a|^(2) +|b|^(2) +|c|^(2) + 2(0)` [from eq. (i)] `= |a|^(2) +|b|^(2) +|c|^(2)` |
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