1.

When does `|vec(a)+vec(b)|=|vec(a)|+|vec(b)|` hold?

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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