# 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?

Correct result:

u3 =  7.348
u3 =  -7.348

#### Solution:

$|u|=12 = \sqrt{ 3^2+9^2 + u_3^2 } \ \\ 12^2 = 3^2+9^2 + u_3^2 \ \\ u_3^2 = 54 \ \\ u_3 = \pm 7.348$
$u_3=-\sqrt{ 12 \cdot \ 12-3 \cdot \ 3-9 \cdot \ 9 }=-7.348$

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