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Question
If D is the midpoint of the aide BC of a triangle ABC, prove that `vec"AB" + vec"AC" = 2vec"AD"`
Solution
Given D is the midpoint of the side BC of a triangle ABC
To prove: `vec"AB" + vec"AC" = 2vec"AD"`
Since D is the midpoint of BC,
We have `vec"BD" = vec"DC"`
From the figure,
`vec"BD" = vec"BA" + vec"AD"`
`vec"CD" = vec"DA" + vec"AC"`
`vec"BD" = vec"CD"`
∴ `vec"BA" + vec"AD" = vec"DA" + vec"AC"`
`- vec"DA" + vec"AD" = vec"AC" - vec"BA"`
`vec"AD" + vec"AD" = vec"AC" + vec"AB"`
∴ `vec"AB" + vec"AC" = 2vec"AD"`
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