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=32+92+u32 122=32+92+u32 u32=54 u3=±7.348|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
u3=12 123 39 9=7.348u_3=-\sqrt{ 12 \cdot \ 12-3 \cdot \ 3-9 \cdot \ 9 }=-7.348

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For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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