Please do the following questions handwritten

6. Consider the ellipse 12 6 (a) Show that the point P(x, y) = (-V6, v3) lies on the ellipse. (b) Write down parametric equations that define the ellipse and determine a param- eter value corresponding to the point P. (c) Use parametric differentiation to find the slope of the tangent line at P. 7. Suppose v = 2i - 4j + 4k and b = 3i + j + 2k. (a) Find projov. (This is the vector component of v in the direction of b. ) (b) Find v = v - projov. Show that v . b =0. What vector is represented by v-? 8. Given u = (1, 2, -2), v = (3, -1, 2), w = (2, 0, 3): (a) Find a unit vector orthogonal to both u and v. (b) What is the volume of the parallelepiped spanned by u, v, w