If two vectors ` vec aa n d vec b` are such that `|veca|=2, |vecb|=3 and veca.vecb=4,` . , Find ` vec a- vec b|dot`

Explanation

We have , `|overrightarrow{{a}}|=2 quad|overrightarrow{{b}}|=2 overrightarrow{{a}} cdot overrightarrow{{b}}=4`


Applying square


`|vec{a}-vec{b}|^{2}=(vec{a}-vec{b}) cdot(vec{a}-vec{b}) `


`=vec{a} cdot vec{a}-vec{a} cdot vec{b}-vec{b} cdot vec{a}+vec{b} cdot vec{b} `


`=vec{a} cdot vec{a}-vec{a} cdot vec{b}-vec{a} cdot vec{b}+vec{b} cdot vec{b} `


`=vec{a} cdot vec{a}-2 vec{a} cdot vec{b}+vec{b} cdot vec{b} `


`=|vec{a}|^{2}-2 vec{a} cdot vec{b}+|vec{b}|^{2} `


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