Please solve all problems step by step with hand-written.

Answers must be organized and legible. Points may be deducted if anything is unclear about the process of your work. Points will be deducted for incomplete reasoning and disorganized work (even if your answers are correct). If you have any diiculties/ questions, you are encouraged to discuss these problems with me. Late assignments must go into the Late Assignment Dropbox on Canvas. . (5 points) Particle 1 starts at point (3,1,1) and particle 2 starts at point (10,5, 4); at t = 0, both particles begin to move along linear paths. After 1 second, particle 1 is at point (4, 3, 4) and particle 2 is at (8, 5,3). (a) Do the paths of the particles intersect? Show all work. (b) Will the particles collide? Show all work. Answer: (a) (b) 2. (5 points) A plane ies with velocity v = (220, 9[), 10) km/h. A wind is blowing out of the northeast 3. (5 points) Consider the tetrahedron (a 4esided pyramid whose faces are all triangles) with vertices at with velocity w = (30,30,0) km/h. A = (1,0,0), B = (0,2,0), C = (0,1,3), and D = (2,2,0). Calculate the surface area and the volume of the tetrahedron.(Hint: You may use the fact that the volume a tetrahedron is exactly one-sixth of (a) Express the wind vector as a sum of vectors, one parallel to the plane's velocity, one perpendicular the Volume of the parallelepiped generated by the same vectors) to it (b) Is the parallel part of the wind blowing with or against the plane? (c) If we account for both v and w, What is the direction vector that describes the actual motion of the plane? Surface Area =