1. a) Determine the symmetric equations for the line throughP(-3, -3, 2)and parallel to the line with equation = (6, 1, -1)+ t(2, 1, 3). b) Determinetwo(2) other points on this line.
2. Find the value ofkso that the lines below are perpendicular -33-1=+62=+32and+74=+8-2=+9-3
3. Determine parametric equations for the plane through the pointsA(2, -4, 1), B(-1, 1, 3), andC(3, 3, 2).
4. Determine a vector equation for the plane that is parallel to the yz-plane and passes through the point(4, -1, 3).
5. Determine a scalar equation for the plane through the pointsM(1, 2, 3)andN(3 ,-2, -1)that is perpendicular to the plane with equation3x + 2y + 6z + 1 = 0.
6. Show that the line with parametric equationsx = 3 + 8t, y = 5 + t, z = 1 + 3tdoes not intersect the plane with equation2x y 5z 2 = 0.
7. Determine the intersection, if any, of the planes with equationsx + y - z + 12 =0and2x + 4y - 3z + 8 = 0.
8. Solve the following system of equations and give a geometrical interpretation of the result. x - y + z = -2 2x - y 2z = -9 3x + y - z = 2
9. Give a geometrical interpretation of the intersection of the planes with equations x + y 3 = 0 y + z + 5 = 0 x + z + 2 = 0
10. Determine a scalar equation for the plane that passes through the point(3, 1, 1)and is perpendicular to the line of intersection of the planes 2x + y - z + 5 = 0andx + y + 2z + 7 = 0.
11. Explain why there are an infinite number of vector and parametric equations for a line.