Question: 16. Consider the plane: [x, y, z] = [2, 4, -3] + s[1, -1, 4] + t[2, 3, -1] A) Find a point on the

16. Consider the plane: [x, y, z] = [2, 4, -3] + s[1, -1, 4] + t[2, 3, -1] A) Find a point on the plane (other than the point already in the equation). B) Determine a normal vector for the plane. 17. Write the scalar equation of the plane that has normal vector [1, 3, -4] and also contains the point (-2, 4, 1). 18. Determine the shortest distance between the point and the line: Point: (5, -3, 2) | Line: [x, y, z] = [1, 2, 3] + t[4, 5, 6] 19. Consider the three planes: x1: x+ 2y+ z -3 =0 72: 2x - y - 3z - 1 = 0 73: 5x + y - 2z = 0 A) Calculate the triple scalar product of their normal vectors (n1 x 12 . 13 ) and state what that means about the interaction of the planes. B) Solve the system of equations to determine the point of intersection (or line of intersection)

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