If ` vec a ,\ vec b ,\ vec c` are position vectors o the point `A ,\ B ,\ a n d\ C` respectively, write the value of ` vec A B+ vec B C+ vec A Cdot`

Explanation

We have given
` vec a ,\ vec b ,\ vec c`
are position vectors to the point `A ,\ B ,\ a n d\ C`.

We get `triangle ABC`

By triangle law of vector addition

`vec{AC}=vec{AB}+vec{BC}`

To find
`vec A B+ vec B C+ vec A C`

`Rightarrow vec A B+ vec B C+ vec A C = vec AC+ vec AC`

`=2 vec AC`

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