\(f(x,y,z)=7xy+yz+4xz-48=0\) (2,2,2)

Tangent direction is \((P_x,P_y,P_z)\)

\(P_x=7y+yz,\ P_y=7x+z,\ P_z=y+4x\)

at (2,2,2)

\(P_x=22,\ P_y=16,\ P_z=10\)

(22,16,10)

\(\Rightarrow x(t)=(2,2,2)+t(22,16,10)\)

\(\Rightarrow22(x-z)+16(y-z)+10(z-z)=0\)

\(22x+16y+10z-96=0\)

Tangent direction is \((P_x,P_y,P_z)\)

\(P_x=7y+yz,\ P_y=7x+z,\ P_z=y+4x\)

at (2,2,2)

\(P_x=22,\ P_y=16,\ P_z=10\)

(22,16,10)

\(\Rightarrow x(t)=(2,2,2)+t(22,16,10)\)

\(\Rightarrow22(x-z)+16(y-z)+10(z-z)=0\)

\(22x+16y+10z-96=0\)