1. Consider two lines L1: r = (2,0,0) + t(1,2,−1) and L2: r =(3,2,3) + s(p,q,1) Find a relationship between p and q [independent of s and t] that ensures that L1 and L2 intersect. i proceeded like any other interesection of line question but got stuck when i got single equations with 3 unknowns (including p and q) 2. The position vectors of the points A and B, with respect to the origin O, are 2i−3j+3k and 5i + j+ck respectively, where c is a constant. The point C is such that OABC is a rectangle. (a) Find the value of c (b) Find the point C how do i find c? if i had the exact coordinates of B, im pretty sure developing an equation like OA = CB would give be the point C (which is part b)) 3. In the following system of equations, k is a real number. x−2y+z=4 x−y−z=3 x+y+kz=1 (a) Determine the value(s) of k for which the system of equations has (i) exactly one solution (ii) infinitely many solutions should i solve this using a standard matrix? what happens when i get down to x = something, y = something, z = something/k. i don't know really what to do differently for i) and ii), what would each part entail? i know i haven't shown a tremendous amount of work but i'm not the greatest thinker and i really have a deficiency of knowledge in this area. thanks for any help given!