Find a vector equation and parametric equations for the line. (use the parameter t.) the line through the point (0, 11, −8) and parallel to the line x = −1 + 4t, y = 6 − 3t, z = 3 + 7t

x=4t

y=11-3t

z=-8+7t

Step-by-step explanation:

The line is parallel to x=-1+4t, y=6-3t, z=3+7t.

Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter). So in this case, the direction is (4,-3,7); this is also the direction of the missing line because they are parallel.

The vector equation of a line is given by:

where v is the direction vector, and is a point of the line.

So, for this case, the line pass for the point (0, 11, −8):

With the direction, the vector equation is:

The parametric equations are just the simplification of the vector equation:

x=4t

y=11-3t

z=-8+7t

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

15

step-by-step explanation: