Questions: Question 5. Q5)a) Parallel project the following points onto the plane x=2 : i) (2,3,0) iii) (3,4,3) v) (2,4,6) ii) (3,3,3) iv) (-1,1,-2) vi) (0,-2,0) Q5)b) Graph the projected points from Q5)a) on the x=2 plane given below:

Solution Steps

To project a point (x, y, z) onto the plane x = 2, we simply replace the x-coordinate with 2. The y and z coordinates remain unchanged.

i) (2, 3, 0) projected onto x=2 becomes (2, 3, 0). ii) (3, 3, 3) projected onto x=2 becomes (2, 3, 3). iii) (3, 4, 3) projected onto x=2 becomes (2, 4, 3). iv) (-1, 1, -2) projected onto x=2 becomes (2, 1, -2). v) (2, 4, 6) projected onto x=2 becomes (2, 4, 6). vi) (0, -2, 0) projected onto x=2 becomes (2, -2, 0).

The given graph represents the plane x=2. The y-axis represents the y-coordinate, and the z-axis represents the z-coordinate. Since we are on the x=2 plane, all points will have an x-coordinate of 2.

We plot the points from Step 1, treating the y-coordinate as the horizontal axis and the z-coordinate as the vertical axis.

i) (2, 3, 0) is plotted at (3, 0). ii) (2, 3, 3) is plotted at (3, 3). iii) (2, 4, 3) is plotted at (4, 3). iv) (2, 1, -2) is plotted at (1, -2). v) (2, 4, 6) is plotted at (4, 6). vi) (2, -2, 0) is plotted at (-2, 0).

Final Answer