Find an equation of the tangent plane to the given surface at the specified poin

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Let f(x,y,z)=xe^y(cosz)-z=8=> grad f(8,0,0)=i+8j-k, where i,j,k are the unit vectors in the x,y,z directions. Let r=xi+yj+zk be a point on the tangent plane, then the dot product of [(x-8)i+yj+zk] & grad f(8,0,0)=0=> (x-8)+8y-z=0=> x+8y-z=8 is the tangent plane. Let p(x,y,z) be a point on the normal line, then (x-8)i+yj+zk=t(i+8j-k), where t is a scalar. r=(t+8)i+8tj-tk is the vector equation of the normal line. where r=xi+yj+zk. (x-8)/1=y/8=z/(-1) is the Cartesian form of the normal lin

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