If two vectors ` vec aa n d vec b` are such that `| vec a|=2,| vec b|=3a n d vec adot vec b=4` , find `(vec a- vec b)`

Explanation

`|overarrow{{a}}|=2 quad|overarrow{{b}}|=2 overarrow{{a}} cdot overarrow{{b}}=4`


Using 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}`

`
=2^{2}-2 times 4+3^{2}`

`
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