Q63Single correct2 Marks7 Aug 2022

Consider the function f(x, y) = x^2 + y^2. Which of the following affine subspaces represent the tangent line at the point $(1, 2)$ in the direction of the vector $(1, 1)$ ?

A

{(x, y, z) in $\mathbb{R}^3$ | (x - 1)/(1/sqrt(2)) = (y - 2)/(1/sqrt(2))}

B

{(x, y, z) in $\mathbb{R}^3$ | (x - 1)/(1/sqrt(2)) = (y - 2)/(1/sqrt(2)) = (z - 5)/(6/sqrt(2))}

C

{(x, y, z) in $\mathbb{R}^3$ | (x - 1)/(1/sqrt(2)) = (y - 2)/(1/sqrt(2)) = (z - 5)/(1/sqrt(2))}

D

{(x, y, z) in $\mathbb{R}^3$ | x/(1/sqrt(3)) = y/(1/sqrt(3)) = z/(1/sqrt(3))}