In R2 plot and describe the set of all points P whose position vector is of the form
p = s(1, 1) + t(−1, 1), 0 ≤ s, t ≤ 1
To plot and describe the set of all points P whose position vector is of the form p = s(1, 1) + t(-1, 1), where 0 ≤ s, t ≤ 1, we can break it down into steps:
Step 1: Determine the range of values for s and t
Given that 0 ≤ s, t ≤ 1, it means both s and t can take values between 0 and 1 inclusive.
Step 2: Find the coordinates of P for different values of s and t
To find the coordinates of P, we can substitute the given values of s and t into the equation p = s(1, 1) + t(-1, 1). Let's calculate a few points:
When s = 0 and t = 0:
p = 0(1, 1) + 0(-1, 1) = (0, 0)
When s = 1 and t = 0:
p = 1(1, 1) + 0(-1, 1) = (1, 1)
With similar calculations, we can obtain more points.
Step 3: Plot the points on a graph
Now, let's plot the obtained points on a graph with the x-axis and y-axis representing the coordinates.
Point (0, 0) is plotted at the origin.
Point (1, 1) is plotted at (1, 1).
By connecting these two points, we can see that the set of all points P forms a line segment between (0, 0) and (1, 1).
Step 4: Describe the set of all points P
The set of all points P whose position vector is of the form p = s(1, 1) + t(-1, 1), where 0 ≤ s, t ≤ 1, is a line segment connecting the points (0, 0) and (1, 1). This line segment starts at (0, 0) and ends at (1, 1).