Describe in words the lines having the following parametric equations. Sketch the lines.
c)
x = -5
y = 2 + t
z = 2 + t
I don't get this question, please tell me how to retrieve the answer and not just the answer!
This is one line in 3-D, you are not dealing with "lines".
In a set of parametric equations, which describe one line, each equation tells you about the behaviour of each of the variables,
so the first one tells you about the x,
the second about the y, etc
from your equations I can tell that the line passes through the point (-5,2,2) and has direction (0,1,1)
by giving any values to t, the parameter, you can create a table of points, which will form a straight line in 3-D
eg. let t=1
x=-5
y=3
z=3 so new point is (-5,3,3)
let t=5
x = -5
y=7
z=7 new point is (-5,7,7)
if you roll a fair number cube 30 times ,how many would you expect to roll a number that is a multipule of 3.
To describe the lines with the given parametric equations and sketch them, you can follow the steps below:
1. The given parametric equations represent a line in three-dimensional space. The variables x, y, and z represent the coordinates of points on the line, and the parameter t determines the position on the line.
2. Start by focusing on the x-coordinate equation: x = -5. This equation means that the x-coordinate of any point on the line is always -5, regardless of the value of t.
3. Next, consider the y and z-coordinate equations: y = 2 + t and z = 2 + t. These equations indicate that the y-coordinate and z-coordinate of any point on the line will be equal and will increase linearly with the value of t. The initial value for both y and z is 2.
4. With this information, you can interpret the line as follows: It is a vertical line that runs parallel to the y and z axes, passing through the point (-5, 2, 2). As t increases, the line extends infinitely in the positive y and z directions.
5. To sketch the line, you can plot a point at (-5, 2, 2) as the starting point. Then, draw a vertical line extending upwards and downwards from that point to represent the infinite extent of the line in the y and z directions.
By following these steps, you should be able to understand the description of the lines and sketch them accurately.