A static (i.e. time-independent}, harmonic, vector disturbance in three dimensions can be written as 1|I{r} = A cos-(kw) where r = xi + + :li is the position vector from the origin to the coordinates (x, y, :)= and { i, i ll) are the Cartesian unit vectors. Beth A {amplitude vector} and k (propagation vector) are constant vectors, meaning they do not depend on r. (a) Write an equation for the locus of points r that lie on the set of parallel planes with 1|!(r) = A. The equation should be expressed in terms of (x= y, z) and A}, kg kg) and an integer n that labels the succession of planes. What is the perpendicular distance between two adjacent such planes? Give your answer in terms of the magnitude of the propagation vector k. (5 points} (b) Rewrite this function as a traveling plane wave disturbance I|I{r, I) in three dimensions. Assume that the wave has amplitude vector A: wavelength (spatial period) It, temporal period 1:, and direction cosines of k given by (his, as, so) = (or, [3, v}. Please give your answer only in terms of: A, (cs, [3, y], FL, I, (I, y, :}, and if. Hint: Start by writing the propagation vector k as k = lm's) = (EnlekHc). (10 points)