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vec(a) , vec(b), vec(c ) are three vectors of which every pair is non collinear. If the vector vec(a)+vec(b) and vec(b)+vec(c ) are collinear with vec(c ) and vec(a) respectively then vec(a) + vec(b) + vec(c ) is :- |
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Answer» Unit vector `implies bar(a) + bar(b) + bar(c ) = (t_(1)+1) bar(c )` ……..(i) `bar(b)+bar(c )=t_(2) bar(a)` `implies bar(a) + bar(b) + bar(c ) = (t_(2)+1) bar(a)` ……..(ii) from (i) and (ii) `(t_(1)+1) bar(c )=(t_(2)+1)bar(a)` but `bar(a) and bar(c )` are non-collinear `:. t_(1) + 1 = t_(2) + 1 = 0` `implies t_(1) = t_(2) = -1` PUT `t_(1) = -1` in (i) `bar(a) + bar(b) + bar(c ) = 0`. |
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