struggling with these problems: 1. determine if the following are: i) collinear: A(0, 3, 2), B(1, 5, 4) and C(3, 9, 8) ii) coplanar: A(1, 4, −5), B(2, 12, −8), C(4, 6, − 4) and D(5, 3, −2) i know that TWO vectors are collinear if it is possible to express one as a scalar multiple of the other. i think that with three vectors, it would be the same; that one vector could be expressed as a combination of the other two (i.e. A = kB + tC). if i found consistent answers for k and b, would that mean that all three are parallel? similarly for ii), im assuming that 4 points are coplanar if one can be exprssed as a combination of the other three (i.e. A = kB + sC + tD), but this would yield 3 equations with 3 unknowns which i do not know how to solve for...is this method wrong then? 2. vectors u=(i+j+k) and v=(i−2j+k), find a vector w, of length sqrt(2), that is perpendicular to both u and v. im guessing i do cross product to find a vector perpendicular to both u and v and then find a vector parallel to the result of the cross product that has magnitude sqrt(2). how i would i express this in an equation to solve for the coordinates of w?