Let W $=$span$\{$~v$1,$ ~v$2,$ ~v$3\},$ where ~v$1=$

$$

$$

$$

$$

$1$

$2$

$0$

$2$

$$

$$

$$

$,$ ~v$2=$

$$

$$

$$

$$

$0$

$6$

$4$

$6$

$$

$$

$$

$,$ and ~v$3=$

$$

$$

$$

$$

$3$

$5$

$1$

$7$

$$

$$

$$

$.$

$($a$)$ Show that the set of vectors B $=\{$~v$1,$ ~v$2,$ ~v$3\}$ forms a basis for W $.$

$($b$)$ Determine whether the set of vectors B is orthogonal. Show your work.

$($c$)$ Find the orthogonal projection of vector ~u $=$

$$

$$

$$

$$

$5$

$2$

$4$

$3$

$$

$$

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$$ onto W $.$

$($d$)$ Use your answer for part $($c$)$ to determine whether the vector ~u is in W $.$