Question

Suppose L is the line in R3 defined by
x = t + 2
y = t + 1
z = 1:
Choose the correct statement(s).
A. (2; 1; 1) is a point on the line L:
B. The vector (3; 3; 0) is parallel to L:

Answer 1

for t=0, you get x= 2, y=1, z= 1
so choice A is correct
we can write the equation as
P= (1,1,0)*t + (2,1,1)
where P is a point in 3-D
the "direction vector" is (1,1,0)
and any vector parallel to it is a scaled version of (1,1,0)
example: 3(1,1,0)= (3,3,0) is a parallel vector.

Answer 2

Why is answer b incorrect

Answer 3

I think b is correct, the vector (3,3,0) is parallel to the line L

Answer 4

Thanks for the response. What software did you use to create the graph

Answer 5

geogebra (it's free)

Answer 6

Thanks for the info