Question

Find the tangent line to the curve that is the intersection of the surfaces ty+yz + zz – 3 = 0 and sin(xyz) = 1 - 3y + 2z at the point (3,1,0). Maximum size for new files: 20MB

Answer 1

The tangent line is in vector form given

0. let, Now (3,1,0)=(1,3,4) F(X,Y,Z) = xy +72+2x-31 G20, 2) a Simay 2) -x+34 - 22 27F(2,1,2) = {y+2,*+2, x+y) FGC2,4,2)=(72603(x4 2)-', x2603 (xyz) +3, xy Cos (xyz) -2) PG(3,1,0) = (-1,3,1) Since Coscojal The cross product of these two gradient is a rector that is tangent to both "Surfaces f and G at the point (3,1,0). 9F3,1,0) X9 G (3,1,0) = î ? now 3 4 3 l =-9€ - 59+ 6h So, the tangent line to the curve of intersection of toro susfaces at the point (3,1:0) is a line that is (-92-5ğ tox) and passed by 31,0).