Chapter 11, Problem 2RE

(a) Sketch vectors u and v for which $\text{u}+\text{v and u}-\text{v}$ are orthogonal.

(b) How can you use vectors to determine whether four points in 3-space lie in the same plane?

(c) If forces ${\text{F}}_{\text{1}}={\text{i and F}}_{\text{2}}=\text{j}$ are applied at a point in 2-space, what force would you apply at that point to cancel the combined effect of ${\text{F}}_1{\text{ and F}}_{\text{2}}?$

(d) Write an equation of the sphere with center $\left(1,-2,2\right)$ that passes through the origin.