Answer
$(5,-1,2),\frac{1}{5}(5,11,-7)$
Work Step by Step
We are given: $x_1=(5,-1,2)\\
x_2=(7,1,1)$ in $R^3$
We can see that $x_1$ and $x_2$ are linearly independent. Thus, $S=\{(5,-1,2),(7,1,1)\}$ is a basic for span of the set $S$.
According to Gram-Schmidt process, we have:
$v_1=x_1=(5,-1,2)\\
v_2=x_2-\frac{}{||v_1||^2}x_1\\
=(7,1,1)-\frac{}{||(5,-1,2)||^2}(5,-1,2) \\
=(7,1,1)-\frac{7.5+(-1).1+2.1}{5^2+(-1)^2+2^2}(5,-1,2)\\
=(7,1,1)-\frac{6}{5}(5,-1,2)\\
=\frac{1}{5}(5,11,-7)$
Hence, a corresponding orthonormal basic for span $S$ is: $(5,-1,2),\frac{1}{5}(5,11,-7)$
