$($b$)$ Apply PCA to $3$ data points in $2-$D space, $(1,1),(2,2)$ and $(3,3).$

$($i$)$

What is the first principal component?

$($i$1)$

If we want to project the original $3$ data points into the $1-$D space by the first principal component, what is the variance of the projected data?