be0f75…: “With a tall trapezoid”

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Find a positive value for $a$ so the vector $\vec {u} = \vector {2,a,5}$ has magnitude $17$ . $a= \answer {2\sqrt {65}}$

We can compute $|\vec {u}|$ in terms of $a$ and find:

$|\vec {u}| = \sqrt {\answer {29+a^2}}$

Setting $|\vec {u}| = 17$ gives:

$17 = \sqrt {\answer {29+a^2}} \\$

Square both sides to obtain:

$\answer {289} = \answer {29+a^2}$

Solving for $a^2$ gives:

$a^2 = \answer {260}$

Now, find $a$ .