10.1.8 Find a vector having the gives length and in the direction from the first point to the second. Length: 12. First point: (-4, 5, 1). Second point: (6,2,-3). 10.1.12 Find parametric equation of the line containing the given points: (2,5,1), (6, 1, -2) 10.2.6 Compute the dot product of the vector and the cosine of the angle between them. Also determine if the vectors are orthogonal. i+j+2k, i-j+2k 10.2.8 Find the equation of the plane containing the point and having the given vector as a normal vector. (-1,0,0), i-2j 10.2.14 Find the projection of v onto u. v = 5i + 2j - 3k, u = i - 5j+2k 10.3.4 Compute Fx G and G x F. F8i6j, G = 14j 10.3.8 Determine if the points are collinear. If they are not, find an equation of the plane containing these points. (0,0,2), (4,1,0), (2,-1,-1) 10.3.12 Find a vector normal to the plane. There are infinitely many normal vectors for each plane (all parallel to each other). x-3y+2x=9 In each of problem, determine whether S is a subspace of Rn 10.4.1. S consists of all scalar multiples of 10.4.4. S consists of all vectors in R8 of length less than 1.