Question

A) determinine whether the plane 2x-y+z=2 and the line with parametric equation x=2-t, y= 1+3t, z=4t intersect or are parallel. B) if they intersect find the point of intersection. if they are parallel find their distance

Answer 1

any clue how to go on these problems?

Answer 2

2x-y+z=2 =>2-t(2)- 1+3t+4t=2

Answer 3

t=1
if plug back i will get 2=2

Answer 4

so they intersect.

Answer 5

how i going to find the pts of intersection

Answer 6

You just plug t=1 back into the given parametric equation and that's your point of intersection.

Answer 7

(1, 4, 4) ?

Answer 8

yes

Answer 9

part a they intersect and the pts inteserction 1, 4, 4 for part b

Answer 10

yes

Answer 11

ok ty @Spacelimbus

Answer 12

you're welcome