Calculus Help

1. a) Determine the symmetric equations for the line through PY-3, -3, 2) and parallel to the line with equation F = (6, 1, -1) + t(-2, 1, 3). b) Determine two (2) other points on this line. All 11 please 2. Find the value of k so that the lines below are perpendicular F 3 243 3k-1 2 / and 2k = 3. Determine parametric equations for the plane through the points A(2, -4, 1), 8(-1, 1, 3), and C(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 points M(1, 2, 3) and N(3, -2, -1) that is perpendicular to the plane with equation 3x + 2y + 62 + 1 = 0. 6. Show that the line with parametric equations x = 3 + 8, y= -5 +t z = 1 + 3: does not intersect the plane with equation 2x - y - 5z - 2 = 0. 7. Determine the intersection, if any, of the planes with equations x + y - 2 + 12 =0 and 2x + 4y - 32 + 8 = 0. 8. Solve the following system of equations and give a geometrical interpretation of the result. X-y+2=-2 2x - y - 2z =-9 3x y-20-2 9. Give a geometrical interpretation of the intersection of the planes with equations x*y-3-0 1 +2 +5=0 X+2+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-2 + 5 = 0 and x + y + 2z + 7 =0. 11. Explain why there are an infinite number of vector and parametric equations for a line