(a) find parametric equations for the line through (3, 1, 8) that is perpendicular to the plane x − y + 4z = 7. (use the parameter t.) (x(t), y(t), z(t)) = (b) in what points does this line intersect the coordinate planes?
xy-plane (x, y, z) =
yz-plane (x, y, z) =
xz-plane (x, y, z) =

• (x, y, z) = (3+t, 1-t, 8+4t) . . . equation of the line

• xy-intercept (1, 3, 0)

• yz-intercept (0, 4, -4)

• xz-intercept (4, 0, 12)

Step-by-step explanation:

The line's direction vector is given by the coordinates of the plane: (1, -1, 4). So, the parametric equations can be ...

(x, y, z) = (3, 1, 8) + t(1, -1, 4) . . . . . parametric equation for the line

or

(x, y, z) = (3+t, 1-t, 8+4t)

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The various intercepts can be found by setting the respective variables to zero:

xy-plane: z=0, so t=-2. (x, y, z) = (1, 3, 0)

yz-plane: x=0, so t=-3. (x, y, z) = (0, 4, -4)

xz-plane: y=0, so t=1. (x, y, z) = (4, 0, 12)

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068