Suppose That $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$

Multiple Choice

Suppose that $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$ Find a normal vector to the tangent plane of f at the point (1, 1) .Select all that apply.

A) $5 \vec { i } + 5 \vec { j } - \vec { k }$
B) $5 \vec { i } + 5 \vec { j } + \vec { k }$
C) $- 5 \vec { i } - 5 \vec { j } + \vec { k }$
D) $- 5 \vec { i } + 5 \vec { j } + \vec { k }$