1 MATH 1300 ASSIGNMENT PROBLEMS (UNIT 2) Solutions 1. Let P = (1, 3, –1), Q = (2, 1, –2) and R = (–2, 1,–3) be 3 points in (a) Find the components of the vector PQand PR(b) Find a set of parametric equations for the line through the points P and R. (c) Use the vectors PQand PRto find a normal vector to the plane through the 3 points P, Q and R. (d) Find a standard form equation of the plane through the 3 points P, Q and R. R3. . Solution: v. 2t. .
2  2. Let 2: 3226and: 239xyzxyzππbe two planes in 3. (a) Find a normal vector 1nto the plane1πand a normal vector 2nto the plane2(b) Find the cosine of the dihedral angle between the planes 1πand 2(c) Find a vector vparallel to the line of intersection of the planes 1πand 2(d) Find the point on the line of intersection of the planes 1πand 2πwhose y-coordinate is 0. (e) Use the results from parts (c) and (d) to find a set of parametric equations of the line of intersection of the planes 1πand 2π1Rπ. π. π. .