Find a line that lies entirely in the set defined by the equation x2 + y2 − z2 = 1.

We want to find a line that lies in the set defined by x^2 + y^2 - z^2 = 1

That line can be <1, t, t>.

So we want to have a line that is defined by the given restriction.

We can rewrite the restriction as:

x^2 + (y^2 - z^2) = 1

Now we can add another restriction (just to find the line) that is defining:

y = z (notice that if we fix the value of x, this will define a line).

Then we will have:

x^2 + (y^2 - y^2) = 1

x^2 = 1

Now we can fix a value for x, for example x = 1

Then our line is defined by:

y = z and x = 1.

Writing it in vector form we would have something like:

<1, t, t>

Replacing that in the restriction, we get

1^2 + t^2 - t^2 = 1 + 0 = 1

As expected.

If you want to learn more, you can read:

link

Step-by-step explanation:

A line is a one-dimensional figure that has no thickness and extends infinitely in both directions.

A line segment is a line that has two end-points and a ray is a line that has one end-point.

Given equation is

To find : a line that lies entirely in the set defined by the given equation.

Solution:

Take

Check:

Therefore, satisfy the given equation.

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?