Question

Use the following steps to find the general equation of the plane that intersects the surface f(x, y) ye2x-y+5 at f(-1,3) Choose any vector ū, u # 0, in the xy-plane that is parallel to neither the x-axis nor the y а) axis. Use a cross product to show that u is parallel to neither axis. Find Duf-1,3) b) Choose any vector v, v *0, in the xy-plane that is orthogonal to u. Use the dot product to show that u and v are orthogonal Find Df(-1,3) d) Define U (u, u2, ||ū||Df(-1,3)) where u=u,i +u2j in part (a). e) (v1, v2, ||||D5f(-1,3)) where v = v, i +v2j in part (c) Define V f) g) Find the general equation of the plane that is determined by the vectors Ū & V and that contains the point at f(-1,3) What geometric relationship does the plane have with the surface f(x,y) ye2x-y+5? Һ)

Answer 1

T y y. + 11 neter axis 2x-y+5 2x-7+52ts Thaus 7arcllel ho u Re xc <6,/-3- <6 - 17 2 17 Vechr Terpendieulor to T+T ( 부후- = 스 orthogomat 1 V2 2 +- the - -)-( u and are - 2 17