7. The equations below define a line L in R3
x + y = 1
x + z = 1
Which of the following equations defines a plane that is perpendicular to L?
|
A. x + y = 1 |
B. x + z = 1 |
C. y – z = 0 |
|
D. 2x + y + z = 2 |
E. x – y – z = 0 |
Solution: The answer is E
Rewrite the equations that define a line L in R3 in parametric form, as follows:
Better yet, write them in vector form as
Now, this line will be a normal to the required plane. Moreover, the plane
ax + by + cz = d has a normal <a, b, c>. The only plane in the selections above that has a normal <1, -1, -1>. is the one in E.