A line passes through the point (9,1, – 1), and is parallel to the vector 7i + 3j + 7k. Find the standard parametric equations for the line, written using the components of the given vector and the coordinates of the given point.

Question 2 a) An aircraft, flying in a straight line, passes through the points (-6,7,2) and (-3,2,3) measured in kilometres. Find the vector form of the equation of the line that describes the flight path of the aircraft. Determine whether or not the aircraft is flying parallel to the ground which is described by the plane -4x + 6y + 42z = 17, where x.y and z are also measured in kilometres. b) A large shade sail is to be hung tautly between the tops of 3 poles. The tops of these poles are located at point A, B, and C as shown in the Figure 1 below. For instance the point A is located at (2, -3,3) m. find the vectors AB and AC and hence the equation of the plane through these three points. 3 m 5 m 2 m 0 2 m 3 m B 3 m 3 m Figure 1: The poles in Q2(b) which the large shade sail is to be hung taughtly between. c) A tunnel is being constructed through a mountain range where the tunnel is being constructed from both ends at the same time. One end of tunnel starts at the point A (80, -287,…

Find a set of parametric equations of the line with the given characteristics. (Use t for the parameter. Enter your answers as a comma-separated list of equations.) The line passes through the point (-6, 8, 7) and is perpendicular to the plane given by -x + 6y + z = 8.

Solve the problem. Describe all solutions of Ax = b, where 2-5 31 A = -2 6-5 70 and b = 310 Describe the general solution in parametric vector form. -3 G -8-17-0

Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.) The line passes through the point (-3, 5, 9) and is perpendicular to the plane given by -x + 3y + z = 5.