Consider the vectors u$=(5,4,2)$u$=(5,4,2),$ v$=(1,4,5)$v$=(1,4,5),$ w$=(0,3,1)$w$=(0,3,1)$ in $3$ dimensions.

$($a$)$ Compute the vector u$$v$$u$$v$.$

u$$v$=$u$$v$=$

$$

$($b$)$ Compute the vector $5$u$+5$v$+6$w$5$u$+5$v$+6$w$.$

$5$u$+5$v$+6$w$=5$u$+5$v$+6$w$=$

$$

You can input square roots like $22$ either as sqrt$(2)$ or $2^(1/2),$ or alternatively enter answers correct to three decimal places.

$($c$)$ Determine the norms $$u$$u$$ and $$v$$v$.$

$$u$=$u$=$v$=$v$=$

CheckQuestion $2$