WeBWorK Standalone Renderer

Each diagram represents the level curves of a function. For each function, consider the point above $P$ on the surface $z = f(x,y)$ .

(a) If the vectors below are normal to the surface at the point $P$ , match each vector to a diagram.

1. $2\vec{i} + 2\vec{j} - 2\vec{k}$

2. $2\vec{i} + 2\vec{j} + 2\vec{k}$

3. $2\vec{i} - 2\vec{j} + 2\vec{k}$

4. $-2\vec{i} + 2\vec{j} + 2\vec{k}$

(b) If the equations below are tangent planes to the surface at the point $P$ , match each equation of the plane to a diagram.

1. $\displaystyle -\frac{x}{2} + \frac{y}{2} - \frac{z}{2} = -7$

2. $2x - 2y - 2z = 2$

3. $-3x - 3y + 3z = 6$

4. $x + y + z = 4$



A		B



C		D

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You can earn 50% partial credit for 4 - 5 correct answers, and 75% partial credit for 6 - 7 correct answers.