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:

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



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