assignment2_solutions - MATH 1300 ASSIGNMENT PROBLEMS(UNIT 2 Solutions[10 1 Let P =(1 3 1 Q =(2 1 2 and R =(2 1,3 be 3 points in R3(a Find the

# assignment2_solutions - MATH 1300 ASSIGNMENT PROBLEMS(UNIT...

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1 MATH 1300 ASSIGNMENT PROBLEMS (UNIT 2) Solutions [10] 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. R 3 . . Solution : v . 2 t . .
2 [10] 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 2π 1 R π . π . π . .