Which of the following points lie on the line with parametric equationsx = 2+4t; y = 3-7t; z = 5t?P(10; -11; 10); Q(-2; 4; 5); R(-2; 10; -5)Select one:a. P and Rb. P, Q and Rc. P and Qd. Qe. None of the other choices is correct

To determine which points lie on the line defined by the parametric equations, we need to substitute the coordinates of each point into the equations and see if we can find a value of t that makes all three equations true.

1. For point P(10; -11; 10):

We substitute x = 10, y = -11, and z = 10 into the equations:

10 = 2 + 4t -11 = 3 - 7t 10 = 5t

Solving these equations for t, we get:

From the first equation, t = (10 - 2) / 4 = 2 From the second equation, t = (3 + 11) / 7 = 2 From the third equation, t = 10 / 5 = 2

Since all three equations give the same value of t, point P lies on the line.

2. For point Q(-2; 4; 5):

We substitute x = -2, y = 4, and z = 5 into the equations:

-2 = 2 + 4t 4 = 3 - 7t 5 = 5t

Solving these equations for t, we get:

From the first equation, t = (-2 - 2) / 4 = -1 From the second equation, t = (3 - 4) / -7 = 1/7 From the third equation, t = 5 / 5 = 1

Since the equations give different values of t, point Q does not lie on the line.

3. For point R(-2; 10; -5):

We substitute x = -2, y = 10, and z = -5 into the equations:

-2 = 2 + 4t 10 = 3 - 7t -5 = 5t

Solving these equations for t, we get:

From the first equation, t = (-2 - 2) / 4 = -1 From the second equation, t = (3 - 10) / -7 = 1 From the third equation, t = -5 / 5 = -1

Since the equations give different values of t, point R does not lie on the line.

So, the correct answer is:

a. P and R