Question

Question #871b4

Answer 1

you are correct

Explanation:

`vec(AB)=vec(AO)+vec(OB)`

`vec(AB)=-vec(OA)+vec(OB)`

putting the vectors in to column vectors for ease of formatting

`vec(AB)=-((1),(3),(p))+((-7),((1-p)) , (p))`

`vec(AB)=((-8),(-2-p),(0))`

substitute for `p`

`vec(AB)=((-8),(-2- -8),(0))=((-8),(6),(0))`

`vec(AB)=-8hatveci+6hatvecj`

`|vec(AB)|=sqrt(8^2+6^2)=10`

unit vector for `vec(AB)`

`hatvec(AB)=vec(AB)/|vec(AB)|`

`hatvec(AB)=1/10(-8hatveci+6hatvecj)=-4/5hatveci++3/5hatvecj`

which is what you got.