Let 
and 
. Determine the projection of 
along 
.
From the definition of projection of along we know the projection of along is the vector 
where
![\[ t = \frac{A \cdot B}{B \cdot B} = \frac{(1,2,3) \cdot (1,2,2)}{(1,2,2) \cdot (1,2,2)} = \frac{11}{9}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-c486c95367903becb926bab1df1fc5b8_l3.png "Rendered by QuickLaTeX.com")
Therefore, the projection of along is
![\[ tB = \frac{11}{9}B. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-f669e253f4dd42dab8fc02adcf852229_l3.png "Rendered by QuickLaTeX.com")
Let and . Determine the projection of along .
From the definition of projection of along we know the projection of along is the vector where
Therefore, the projection of along is