Question

Let L be the line with parametric equations x=-2+t, y=-1+3t, z=1+5t.
Let v=(1,1,1).
Find vectors w1 and w2 such that v= w1 + w2, and such that w1 is parallel to L and w2 is perpendicular to L.

Answer 1

okkk so how can u find w1 parallel to L ?

Answer 2

I posted because I have no clue where to begin. Would be the dot product? Don't know really.

Answer 3

ic , well no problem we can do it together :D

Answer 4

I hope so ^^

Answer 5

I'm ready :p

Answer 6

so the line
L=<x,y,z>
=< -2+t, -1+3t, 1+5t.> =(-2,-1,1)+<1,3,5>t
so this gives u the vector <1,3,5>t which is parallel to the line from the line equation right ?

Answer 7

Right.

Answer 8

Wow, sorry, idk why OPS is being slow for me :T

Answer 9

ok so let w1=<1m,3m,5m> s,t m is a real number

Answer 10

Alright.

Answer 11

next step is how find vector perpendicular to line :)

Answer 12

Let's do it.

Answer 13

so if let w2=<x2,y2,z2>
w2.<1,3,5>=0 (dot product )
cuz they are perpendicular each other , right ?

Answer 14

Amateur question, how can you tell if they are perpendicular?

Answer 15

simply ill show u

Answer 16

assume this is line L

Answer 17

I assume :p

Answer 18

w1 is a vector parallel to L ( given)

Answer 19

w2 is a vector perpendicular to L ( given )

Answer 20

so since w1 || L
then w1 is perp. to w2
got it nw ?