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When does `|vec(a)+vec(b)|=|vec(a)|+|vec(b)|` hold? |
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Answer» Correct Answer - `vec(a) and vec(b)` are parallel or collinear `|vec(a)+vec(b)|=|vec(a)|+|vec(b)|rArr|vec(a)+vec(b)|={|vec(a)|+|vec(b)|}^(2)` `rArr (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|+|vec(b)|+2|vec(a)||vec(b)|` `rArrvec(a).vec(b)+2vec(a).vec(b)+vec(b).vec(b)=|vec(a)|^(2)+|vec(b)|^(2)+2|vec(a)||vec(b)|` `rArr|vec(a)|^(2)+2vec(a).vec(b)+|vec(b)|^(2)=|vec(a)|^(2)+|vec(b)|+2|vec(a)||vec(b)|` `rArr 2(vec(a).vec(b))=2(|vec(a)||vec(b)|)rArr vec(a).vec(b)=|vec(a)||vec(b)|` `rArr |vec(a)||vec(b)|cos theta=|vec(a)||vec(b)|rArr cos theta =1 rArr theta=0^(@)`. `:.` either `vec(a) and vec(b)` are parallel or collinear. |
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