Question 3: [10pt total] Consider the line in 3D space that goes through the points (2,5,-4)...
Question 1: [10pt total] Consider the line through the points (-3,-4) and (1,4). Q1)a) (3pt) Graph the line on the ey-plane below: 6 4 2 6 4 2 0 2 4 6 2 Q1)b) (3pt] Calculate the equation of the line in the form y=mx+b. Equation of the line: Q1)c) (4pt] Calculate a parametrization of the line. Parametrization of the line:
Question 10: [8pt total] Consider the line in 3D space (2,5, 2) +t(-6, 4, 2). 10)a) [4pt] Determine vanishing point of the line when centrally projected onto the plane z = 2: Vanishing point: 10)a)ii) (4pt] Graph the central projection of the line onto the plane z = 2. y 6 2 2 8 -6 -4 -2 0 2 8 -2 61
Question 5. [5pt total] Consider a cuboid in 3D-space that is resting on the ty-plane, with one vertex at the origin, and the vertex farthest from that vertex is at (4,5,3). What are the coordinates of the other 6 vertices? 4 3 (4,5,3) 2 6 1 -2 3 2 -1 2 3 -2 Coordinates:
Question 6: (10pt total] Q6)a) (5pt] Apply a (3,2)-linear-distortion to the following square and sketch the result on the same coordinate axis. 6 4 2 -6 2 0 2 2 -4 -6 Q6)b)i) [2pt] Calculate the area of the original square: Q6)b)ii) [3pt] Calculate the area of the you drew in Q6)a):
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
Question 3 a) Find the cartesian equation of the line that passes through the origin and lies perpen- (3 dicular to the plane 3x - 5y +2z 8. marks] b) Find the cartesian equation of the plane that lies perpendicular to the line 3 marks] and passes through the point 1 cExplain why a unique plane passing through the three points A(-2,-1,-4), B(0,-3,0) [2 marks) and C(2,-5,4) cannot be defined. Question 3 a) Find the cartesian equation of the line...
Question 1 (10 points] Let L be the line passing through the point P=(4, -2,5) with direction vector d=[5, 2, 2]', and let T be the plane defined by –2x-3y=z=-5. Find the point Q where L and T intersect. Q=(0,0,0)
1. (10) Let l be the line in 3-space that passes through the points A=(5,2, -1) and B = (6,0,–7). (a) Find a set of parametric equations for l. (b) Find the unique point P at which l intersects the plane with equation -3.21 + 722 - 2.23 = 11. (c) Let P be the point found in part (b), and let Q = (k, 7, 10) for an unspecified real number k. Determine the value of k for which...
Give the EQUATION of the line in slope intercept form that goes through the points: (4, - 9) and ( - 4, - 5) Preview
Question 7: [20pt total] The points (-4,4,2), (4,4, 2), (4, -4,4), and (-4, -4,4) form the vertices of a rectangle in 3D space. Q7)a) [12pt] Complete the below table by calculate the central and parallel projections of these points onto the plane z = 1. Point Central projection onto z=1 Parallel projection onto z (-4,4,2) (4,4,2) (4, -4,4) (-4,-4,4) Q7)b) (8pt] Sketch both the centrally projected rectangle and the parallel projected rectangle on the coordinate planes below (be sure to...