# 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 =  0

#### Solution:

$a=(2, y, z) \ \\ b=(-1, 4, 2) \ \\ c=(3, -3, -1) \ \\ \ \\ a.b=0 \ \\ a.c=0 \ \\ \ \\ \ \\ \ \\ 2 \cdot \ (-1)+y \cdot \ 4+z \cdot \ 2=0 \ \\ 2 \cdot \ 3+y \cdot \ (-3)+z \cdot \ (-1)=0 \ \\ \ \\ 4y+2z=2 \ \\ 3y+z=6 \ \\ \ \\ y=5 \ \\ z=-9 \ \\ \ \\ y=5$
$z=0$

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