H [3t-2] t+3 [2t-3] (a) Find all values of t for which w and z are orthogonal. 2. Consider the vectors w= and z= (b) Compute the projection of the vector z onto w; your answer should be a vector whose components are expressions in terms of t. (c) Find a point P in R³ such that the points (0,0,0), (1,-1, 1), (4, 5, 1), and P form a rectangle. Explain your reasoning.

The velocity vector of a particle in the xy-plane is (√7, 9e3-3) for all real t. If the position of the particle at t = 1 is (9, 8), then the position vector of the particle is Select one: O.a. ( 21, 3 + 3/3, 303³1-3 + 5) (4) b. 3 4 ○ c. d. 9³-3-1) (+37³½³, 30³-3) 4 Od (-1.3-5) 4 1, 3e

Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R = (0, 1, -1) 8 0-0-0- y = + S 8 Z -4 -6 + t

Part B