Vector perpendicular

Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)

Correct result:

y =  5
z =  -9

Solution:

$$\begin{gathered} a=(2,y,z) \\ b=(-1,4,2) \\ c=(3,-3,-1) \\ a\mathrm{.}b=0 \\ a\mathrm{.}c=0 \\ 2\cdot (-1)+y\cdot 4+z\cdot 2=0 \\ 2\cdot 3+y\cdot (-3)+z\cdot (-1)=0 \\ 4y+2z=2 \\ 3y+z=6 \\ y=5 \\ z=-9 \\ y=5 \end{gathered}$$

$z=(-9)=-9$

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