![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 li](http://img.homeworklib.com/questions/afb5f760-e8c8-11ea-a8de-35775019a06c.png?x-oss-process=image/resize,w_560)
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Question 10: [8pt total] Consider the line in 3D space (2,5, 2) +t(-6, 4, 2). 10)a)...
Question 8: [20pt total] Consider the line (1, -3, -1) + t(1,3,2). Q8)a) [12pt] Complete the...
Question 8: [20pt total] Consider the line (1, -3, -1) + t(1,3,2). Q8)a) [12pt] Complete the table below by calculating the relevant points on the line and their central projections onto the plane x = 2 (the first one is done for you). t Point on line Central projection onto r = 2 t=0 (1, -3, -1) +0(1,3,2) = (1, -3, -1) (2, -6, -2) t=1 t = 10 t = 100 Q8)b) (5pt] Determine vanishing point of the line...
Question 7: [20pt total] The points (-4,4,2), (4,4, 2), (4, -4,4), and (-4, -4,4) form the...
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...
Question 3: [10pt total] Consider the line in 3D space that goes through the points (2,5,-4)...
Question 3: [10pt total] Consider the line in 3D space that goes through the points (2,5,-4) and (2,8,0). Q3)a) [5pt] Calculate a parametrization of the line. Parametrization of the line: Q3)b) (5pt] This line lies on a plane which is perpendicular to a coordinate axis: what equation describes that plane? Equation of the plane:
Question 1: [10pt total] Consider the line through the points (-3,-4) and (1,4). Q1)a) (3pt) Graph...
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 1 (10 points] Let L be the line passing through the point P=(4, -2,5) with...
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)
Question 5. [5pt total] Consider a cuboid in 3D-space that is resting on the ty-plane, with...
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 2 (5%). Let L be a line in 3D such that it is perpendicular to...
Question 2 (5%). Let L be a line in 3D such that it is perpendicular to the plane X - Y - z = 1. Choose the correct answer for vectors which are perpendicular to L. (A) All normal vectors of the plane X – Y – z = 10. (B) All normal vectors of the plane x + 2y + 3z = 3. (C) All vectors parallel to the line (-1,-1,1) ++(-1,-1,1). (D) All vectors parallel to the line...
(a) Find symmetric equations for the line that passes through the point (4, -2, 6) and...
(a) Find symmetric equations for the line that passes through the point (4, -2, 6) and is parallel to the vector (-1, 3, -4) x+ 4-Y+ 2 3 z-6 -4 -(x +4) 3(y 2)-4(z +6). y+2 z-6 3 -(x-4) 3(y +2) -4(z- 6). o4-2-116 = Y - 2-z+6 3 (b) Find the points in which the required line in part (a) intersects the coordinate planes. 5 ,5,0 x ) point of intersection with xy-plane 10 7 point of intersection with...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Exam 2 Version B - Page 5 of 6 Math 8 : Linear Algebra 5. (10 points) Find the projection of b onto the column space of...
Exam 2 Version B - Page 5 of 6 Math 8 : Linear Algebra 5. (10 points) Find the projection of b onto the column space of A where b-2 and - 01
Exam 2 Version B - Page 5 of 6 Math 8 : Linear Algebra 5. (10 points) Find the projection of b onto the column space of A where b-2 and - 01
Question 8: [20pt total] Consider the line (1, -3, -1) + t(1,3,2). Q8)a) [12pt] Complete the table below by calculating the relevant points on the line and their central projections onto the plane x = 2 (the first one is done for you). t Point on line Central projection onto r = 2 t=0 (1, -3, -1) +0(1,3,2) = (1, -3, -1) (2, -6, -2) t=1 t = 10 t = 100 Q8)b) (5pt] Determine vanishing point of the line...
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...
Question 3: [10pt total] Consider the line in 3D space that goes through the points (2,5,-4) and (2,8,0). Q3)a) [5pt] Calculate a parametrization of the line. Parametrization of the line: Q3)b) (5pt] This line lies on a plane which is perpendicular to a coordinate axis: what equation describes that plane? Equation of the plane:
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 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)
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 2 (5%). Let L be a line in 3D such that it is perpendicular to the plane X - Y - z = 1. Choose the correct answer for vectors which are perpendicular to L. (A) All normal vectors of the plane X – Y – z = 10. (B) All normal vectors of the plane x + 2y + 3z = 3. (C) All vectors parallel to the line (-1,-1,1) ++(-1,-1,1). (D) All vectors parallel to the line...
(a) Find symmetric equations for the line that passes through the point (4, -2, 6) and is parallel to the vector (-1, 3, -4) x+ 4-Y+ 2 3 z-6 -4 -(x +4) 3(y 2)-4(z +6). y+2 z-6 3 -(x-4) 3(y +2) -4(z- 6). o4-2-116 = Y - 2-z+6 3 (b) Find the points in which the required line in part (a) intersects the coordinate planes. 5 ,5,0 x ) point of intersection with xy-plane 10 7 point of intersection with...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Exam 2 Version B - Page 5 of 6 Math 8 : Linear Algebra 5. (10 points) Find the projection of b onto the column space of A where b-2 and - 01
Exam 2 Version B - Page 5 of 6 Math 8 : Linear Algebra 5. (10 points) Find the projection of b onto the column space of A where b-2 and - 01
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