2. Displacement vector Af and acceleration vector å are drawn below. The norms of these vectors can be written as A| and lä], respectively. These vectors live in the plane of the paper. The scalars A and B describe lengths. Chosen coordinate System

8. A theme that will later unfold concerns the use of coordinate systems. We can identify the point (x, y) with the tip of the vector drawn emanating from the origin. We can then think of the usual Cartesian coordinate system in terms of linear combinations of the vectors ej = e2 = V2 V1 (2, –3) 42,–3} Figure 2.1.8. The usual Cartesian coordinate system, defined by the vectors ej and e2, is shown on the left along with the representation of the point (2, -3). The right shows a nonstandard coordinate system defined by vectors v1 and v2. The point (2, -3) is identified with the vector — 2е1 — Зе2. If we have vectors v1 = ,v2 = we may define a new coordinate system, such that a point {x, y} will correspond to the vector xv1 + yv2. For instance, the point {2, –3} is shown on the right side of Figure 2.1.8 Write the point {2, –3} in standard coordinates; that is, find r and y such that а. (», у) 3 {2, —3}. b. Write the point (2, –3) in the new coordinate system; that is, find a and b such…

Consider the following vectors: u = (1, −2, −1), v = (-2, 1, 8) Without using the cross product, find a vector n which is orthogonal to both u and U. You need to use a notion from chapter 5 to set up a system of linear equations, then use RREF to solve the system. Explain why this method works.