Given 20 data points in 2-D space whose first principal component is \(u=\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}ight)^{\prime}\).

a. Suppose we add one more data point at \((2,2)^{\prime}\); how would that affect the first principal component?

b. Suppose we add one more data point at \((3,0)^{\prime}\); how would that affect the first principal component?

c. Suppose we add an infinite number of data points at \((5,0)^{\prime}\); how would that affect the first principal component?