Please help me. This are my homework and I am having a hard time on solving this. The answers of the questions are already provided. So you could check your work by that. Also please show all your work. I really appreciate for all your helps.

Here is my questions:

Vectors Problem 1: (Vector Decomposition) A force F = 21 + j - 3k is applied to a spacecraft with velocity vector v = 31 -j. Express F as a sum of a vector parallel to v and a vector orthogonal to v, i.e. F = F + F . Find F and F. (Answer: F = 1.51 - 0.5j, F, = 0.51 + 1.5j - 3k). Problem 2: Given three points, P, (1, 3, 0); P2 (2, -1, 1), P, (3, -5, 2). Determine whether or not the three points lie on a straight line. (Hint: the three points lie on the same straight line if and only if the area of the triangle formed by the three points is 0.) (Ans: these three points lie on a straight line). Planes: Problem 3: Find the plane through A(1, -2,1) and perpendicular to the vector from the origin to A. (Ans: x - 2y + z = 6) Problem 4: Find the distance from the plane x + 2y + 62 = 1 to the plane x + Zy + 62 = 10. (Ans: - 9 41