Activity 2: Derive the expression for the distance between P, and P2. Step 1: Find the magnitude for the AB: HINT: The x-coordinates for A, and B are the same Step 2: Now find |AP, |, and use |AP, and |AB|, and the Pythagorean Theorem to find | P, B|. Step 3: Use | P, B| and | BP2 | and the Pythagorean Theorem to find |P, P2|.Activity 3: The figure shows a line L, in space and a second line L2, which is the ZA projection of Ly on the xy-plane. (a) Find the precise coordinates of the point P on the line Ly . HINT: You'll need to print this out, and use a straight-edge and pencil. P 1 . 0 L2 (b) Locate on the diagram the points x A, B, and C, where the line L1 intersects the xy-plane, the yz- plane, and the xz-plane, respectively. transb sal Activity 4: Find the distance between the spheres x2 + y2 + z2 = 4 and x2 + y? + z? = 4x + 4y + 4z -11 HINT: The distance between two spheres is the length of the line segment connecting their centers minus the sum of their radii.Activity 1: Consider the rectangular box with vertices ABCP FP2 DE. Fill-in the rest of the vertices, if the given vertices for P1, P2, and A are given below. Assume the values x 1, y1, Z1, X2, 12, Z2 are fixed values. P1 (X], )1,Z1) P2 (X2, )2, Z2) E( D( Z F( ) C( ) A (X2, )1, Z1) B( y X