Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously orthogonal to both AB' and AC (b) Find an equation of the plane passing through A, B and C. (c) Find the line of intersection of the plane from part b) and the XZ-plane.

16. Determine the vector equation of each line. a) parallel to the y-axis and through Po(-4, 11) b) perpendicular to 5x - 2y = 3 and through Po(7, 1) c) parallel to x + 6y = 1 and through Po(2,-5) d) parallel to the z-axis and through Po(-4, 3, 7) e) parallel to [x, y, z]= [1, 3, -2] + [5, 2, 1] f) the x-intercept of the line is 3 and the y-intercept is -2

30. Find an equation of the plane that contains the points (-2, 1, 4) and (0, 3, 1) and contains a line parallel to the vector 2i - 4j + 6k.

Let vector a=4i-5j+3k and a point P(2,-1,3). If the length of PQ is equal to the length of vector a, and vector PQ is opposite to vector a, then the coordinate of Q is …  (2,-4,0)  (6,-6,0)  (-2,4,0)  (6,-6,-6) The equation for the plane passing through points (3,2,1),(2,1,-1), and (-1,3,2) is given as follows. 9x + y - z - 16 = 0  x + 9y - 5z - 16 = 0  x - 9y - 5z + 16 = 0  x + 5y - 9z - 16 = 0choose the correct answer